Answer:
72%
Step-by-step explanation:
QT has length 42-24 = 18.
ST has length 42-29 = 13.
The length ST is 13/18 ≈ 72.2% of the length of QT.
Answer:
Probability = 72.2%
Step-by-step explanation:
A number line contains points Q, R, S, and T with coordinated 24, 28, 29, and 42 respectively.
Now if a point lies on QT then the length of QT= coordinate of T - coordinate of Q
= 42 - 24
= 18
If a point lies on ST then the length of ST = coordinate of T - coordinate of S
= 42 - 29
= 13
Now we know Probability of an event = [tex]\frac{\text{Favorable event}}{\text{Total possible events}}\times 100[/tex]
Probability = [tex]\frac{13}{18}\times 100[/tex]
= 72.2%
Therefore, probability that a point chosen on QT will lie on ST will be 72.2%
Solve x − 7y = 8 for x.
A.x = −7y + 8
B.x= −7y − 8
C.x = 7y − 8
D.x = 7y + 8
Answer:
D
Step-by-step explanation:
you need to get the x alone so to do that, you need to add 7y so you do it on both sides and it gives you x=7y+8
The value of the expression x − 7y = 8 will be x = 7y + 8. The correct option is D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression is x − 7y = 8. The value of x will be calculated as below:-
x − 7y = 8
x = 7y + 8
Therefore, the value of the expression x − 7y = 8 will be x = 7y + 8. The correct option is D.
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The number of fish in a lake can be modeled by the exponential regression equation y = 14.08 • 2.08x, where x represents the year. Which is the best prediction for the number of fish in year 5? Round your answer to the nearest whole number. A. 39 B. 548 C. 1464 D. 146
Answer: B. 548
Step-by-step explanation:
You know that the exponential regression equation [tex]y = 14.08* 2.08^x[/tex] models the number of fish in a lake.
You know that the variable "x" represents the year. Therefore, ir order to predict the number of fish in year 5, you need to substitute [tex]x=5[/tex] into the given exponential regression equation.
Then, you get:
[tex]y = 14.08* 2.08^x\\\\y = 14.08* 2.08^5\\\\y=548.17[/tex]
Rounded to the nearest whole number:
[tex]y=548[/tex]
Answer:
The correct answer option is C. 548.
Step-by-step explanation:
We are given that the number of fish in a lake can be modeled by the following exponential regression equation:
[tex] y = 1 4 . 0 8 \times 2 . 0 8 ^ x [/tex]
where [tex]x[/tex] represents the number of year.
We are to determine whether which of the given answer options best predict the number of fish in year 5.
[tex] y = 1 4 . 0 8 \times 2.08^5[/tex]
[tex]y = 548.17[/tex] ≈ 548
3x = 729
Solve for x
plz help. it's urgent. Will mark brainly
Answer: x=243
Step-by-step explanation:
A group of friends go to the movies. The function h(x) represents the amount of money spent where x is the number of friends at the movies. Does a possible solution of (6.5,$95.25) make sense for this function?
Answer:
not really
Step-by-step explanation:
The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.
_____
There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.
No, the solution (6.5,$ 95.25) do not make a sense.
Since, the number of people going for a movie can't be in decimals.
Step-by-step explanation:The function h(x) represents the amount of money spent where x is the number of friends at the movies.
The domain of such a function has to be whole numbers.
Because the number of people that go for a movie must exist as a whole they can't exist in decimals.
( i.e. either no one will go.
1 will go.
2 friends will go and so on)
i.e. the domain is the set of all non-negative integers.
Cube shaped box for packing tape Cube shaped container the edge of the length of the storage container is 2 and 1/2 ft of each block is 1/5 of the storage container what is the volume in cubic feet of one of the shape
Answer:
1/8 ft³
Step-by-step explanation:
Apparently cubic blocks that are 1/5 of 2 1/2 ft on a side are used to fill the cube that is 2 1/2 ft on a side. Then each edge of the block is ...
(1/5) × (5/2 ft) = 1/2 ft
The volume of the block is the cube of that:
(1/2 ft)³ = 1/8 ft³
Please answer this multiple choice question for 27 points and brainliest!!
Answer:
A
Step-by-step explanation:
The equation will be in the form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2.5, 0) ← 2 points on the line
m = [tex]\frac{0-5}{2.5-0}[/tex] = - 2
The line crosses the y- axis at (0, 5) ⇒ c = 5
y = - 2x + 5 or
y = 5 - 2x → A
Lori purchases a new set of watercolor paints and some canvases to create art for her next exhibit. The watercolor paint set costs $15 and the canvases are $24.50 each. If Lori buys 6 canvases, what is the total amount of money she spends for her next exhibit?
Answer:172
Step-by-step explanation:
24.5 times 6 is 157
Plus 15 for the paint is 172 for the TOTAL for ALL she spent
Answer:
The answer is $162.00Step-by-step explanation
write a verbal expression to represent
w^2 =32w
BRAINLIEST!
Verbal expression of w^2 = 32w is:
W to the second power equals 32 with a variable of w.
To the second power means exponent of 2.
Variable is an unknown number represented by a letter. In this case, the variable is "w".
Hope this helps!
- Melanie
Answer:
Step-by-step explanation:
The square of variable w is equal to 32 times that variable.
Which of the following equations is of the parabola whose vertex is at (4, 3), axis of symmetry parallel to the y-axis and focus at (4, -3)?
A.) y+3=1/24 (x+4)^2
B.)y-3=-1/24 (x-4)^2
C.)x-4=-1/24 (y-3)^2
Answer:
B.
Step-by-step explanation:
First thing to determine is how this parabola opens. Up or down? Or left or right?
*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x = line, making this an up or down parabola. Now we need to determine how everything else all fits in.
The standard form of this type of parabola is
[tex]4p(y-k)=-(x-h)^2[/tex]
where p is the distance between the vertex and the focus. If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6. Therefore, p = 6. Filling in then:
[tex]4(6)(y-3)=-(x-4)^2[/tex]
and [tex]24(y-3)=-(x-4)^2[/tex]
Dividing both sides by 24 gives you what you are looking for:
[tex]y-3=-\frac{1}{24}(x-4)^2[/tex]
The equation of the parabola is:
⇒ y - 3 = -(1/24)(x - 4)²
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We can use the standard form of the equation of a parabola with vertex (h, k) and axis of symmetry parallel to the y-axis, which is given by:
(x - h)² = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus.
In this case, the vertex is (4, 3) and the focus is (4, -3).
Therefore, We get;
p = 3 - (-3)
p = 6.
Substituting the values of h, k, and p, we get:
(x - 4)² = 4(6)(y - 3)
Simplifying, we get:
(x - 4)² = 24(y - 3)
Now, we can simplify the equation to match it with the given options:
(x - 4)² = 24y - 72
(x - 4)² + 72 = 24y
y = (1/24)(x - 4)² + 3
Therefore, the equation of the parabola is:
B.) y - 3 = -(1/24)(x - 4)²
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The scatter plot below shows the relationship between the leaf length (x) and leaf width f(x), in mm, of some leaves of a tree:ordered pairs 11, 0.5 and 12, 1 and 13, 1.5 and 14, 2 and 15, 2.5 and 16, 3 and 17, 3.5 and 18, 4 and 19, 4.5 and 20, 5 and 21, 5.5 and 22, 6Which of the following functions is best represented by the scatter plot?f(x) = −5 + 0.5xf(x) = 5 + 0.5xf(x) = x − 10.5f(x) = −x − 10.5
Answer:
The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answer
Step-by-step explanation:
* Lets talk about the scatter plot
- Scatter plots are similar to line graphs in that they use horizontal and
vertical axes to plot data points
- Scatter plots show how much one variable is affected by another.
- The relationship between two variables is called their correlation
- There are three types of correlation:
positive: one variable increases so the other increase
negative: as one variable increases, the other decreases
no correlation: there is no clear relationship between the variables
* Lets solve the problem
- The scatter plot shows the relationship between the leaf length (x)
and leaf width f(x)
- Some leaves of a tree are ordered pairs:
# (11 , 0.5) , (12 , 1) , (13 , 1.5) , (14 , 2) , (15 , 2.5) , (16 , 3) , (17 , 3.5) ,
(18 , 4) , (19 , 4.5) , (20 , 5) , (21 , 5.5) , (22 , 6)
∵ The scatter plot is similar to the line graph
- Lets find the equation which represents the relation between
x and f(x)
∵ The form of the linear equation is y = mx + c, where m is the slope
of the line and c is the y-intercept
- The rule of the slope of the line which passes through points (x1 , y1)
and (x2 , y2) is: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Chose any two points to find the slope of the line
∵ (12 , 1) and (14 , 2) are two points on the line
∴ [tex]m=\frac{2-1}{14-12}=\frac{1}{2}=0.5[/tex]
- Substitute the value of m in the equation
∴ y = 0.5 x + c
- To find c use any point from above and substitute x and y by its
coordinates
∵ Point (16 , 3) lies on the line
∴ 3 = 0.5(16) + c ⇒ simplify
∴ 3 = 8 + c ⇒ subtract 8 from both sides
∴ 3 - 8 = c
∴ c = -5
- Substitute the value of c in the equation
∴ y = 0.5 x - 5
* The best function represented by the scatter plot is f(x) = -5 + 0.5 x
If the system of the linear equations above has infinitely many solutions, and c is a constant, what is the value of c?
A) - 6
B) - 3
C) - 2
D) - 1
1. For the system of linear equations to have an infinite number of solutions, the two lines must cross over an infinite number of times, ie. they would be the same line.
Now, if they are the same line and we were to write out both equations in the form y = mx + c, this would mean that the m value (the gradient) and the c value (the y-intercept) would be the same. Thus, the first step is to write out both equations in the form y = mx + c.
a) Equation 1:
3x - 9y = -6
3x = -6 + 9y (Add 9y to both sides)
3x + 6 = 9y (Add 6 to both sides)
(1/3)x + 2/3 = y (Divide both sides by 9)
Thus, the first equation may be written as y = (1/3)x + 2/3
b) Equation 2:
(1/2)x - (3/2)y = c
(1/2)x = c + (3/2)y (Add (3/2)y to both sides)
(1/2)x - c = (3/2)y (Subtract c from both sides)
(1/3)x - (2/3)c = y (Multiply both sides by 2/3)
Thus, the second equation may be written as y = (1/3)x - (2/3)c.
2. Now that we have both equations in the form y = mx + c, we can look at their gradients and y-intercepts:
Equation 1: gradient = 1/3, y-intercept = 2/3
Equation 2: gradient = 1/3, y-intercept = -(2/3)c
As we can see above, the gradients of the two lines are the same, however for them to be the same line their y-intercepts must also be equal. Thus, we must equate the two y-intercepts to find c:
2/3 = -(2/3)c
1 = -c (Multiply both sides by 3/2)
-1 = c (Multiply both sides by -1)
Thus, if the system of linear equations has infinitely many solutions, and c is a constant, the value of c is -1 (answer D).
The value of 'c' for the given system of the linear equations with infinitely many solutions is - 1.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given system of linear equations are
1. [tex]3x - 9y=-6[/tex]
⇒ [tex]x - 3y = - 2[/tex]
Therefore, [tex]a_{1} = 1, b_{1} = -3, c_{1} = -2[/tex]
2. [tex]\frac{x}{2}-\frac{3y}{2} =c[/tex]
⇒ [tex]x - 3y = 2c[/tex]
Therefore, [tex]a_{2} = 1, b_{2} = -3, c_{2} = 2c[/tex]
For the system of the linear equations with infinitely many solutions,
[tex]2c = -2[/tex]
⇒ [tex]c = -1[/tex]
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NEED HELP WITH A MATH QUESTION WITH FINDING A SURFACE AREA OF A SQAURE PYRAMID
ANSWER
[tex]S.A = 125 {in}^{2} [/tex]
EXPLANATION
The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.
This is given by the formula!
[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]
From the diagram, the base is 5 inches and the height is 10 inches.
We substitute the values to get:
[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]
This simplifies to;
[tex]S.A = 100 + 25[/tex]
[tex]S.A = 125 {in}^{2} [/tex]
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x – x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary. width = 26 ft; area = 364 ft2 width = 26 ft; area = 169 ft2 width = 13 ft; area = 507 ft2 width = 13 ft; area = 169 ft2
Answer:
width = 13 ft; area = 169 ft^2
Step-by-step explanation:
The equation for the area can be factored as ...
A = x(26 -x)
This has zeros at x=0 and x=26. The vertex of this downward-opening parabola will be halfway between those, at x=13. Then the area for a width of 13 feet is ...
A = 13(26 -13) = 13^2 = 169 . . . . ft^2
The maximum area is 169 ft^2, when the width is 13 ft.
_____
You will note that these dimensions make the pen be a square. It can be useful to remember that a square is the rectangle with the largest area for a given perimeter length.
The width that gives the maximum area for the given fencing is 13 feet, and the maximum area is 169 square feet (option B).
Explanation:
The formula given is a quadratic function where x is the width and A is the area. In a quadratic function, the maximum or minimum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a where a and b are the coefficients of the quadratic function. Here, a is -1 and b is 26, therefore the x-coordinate of the vertex is -26/-2*-1 = 13. This means that a width of 13 ft will give the maximum area. To find the maximum area, we substitute x = 13 into the function: A = 26*13 - 13^2 = 169 ft2. So, the width that will give the maximum area is 13 feet and the maximum area is 169 square feet.
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Avery has a total of $12.50 in her piggy bank at home. Each week she takes out $1.25 to ride the city bus. Write an equation representing the balance, c, in the piggy bank, where w, represents weeks.
Answer:
1.25(w)-12.50=C
Where do you find sculptures of great baseball sluggers math worksheet answers?
The sculptures of great baseball sluggers are found in famous places of the city.
Here,
The sculptures of any famous personalities are installed in the places that are frequently visited by the public , so that the it will gain traction.
Thus,
The sculptures of famous baseball players will be available in city malls , museums , parks or baseball stadium.
The players coming to play baseball will be motivated by seeing their idols.
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If carol travels 30 miles and her car averages 48 miles per hour, how long will it take carol to complete the distance?
[tex]\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 48&1\\ 30&x \end{array}\implies \cfrac{48}{30}=\cfrac{1}{x}\implies \cfrac{8}{5}=\cfrac{1}{x}\implies 8x=5 \\\\\\ x=\cfrac{5}{8}\qquad \textit{37 minutes and 30 seconds}[/tex]
What is the equation of the line best fit for the following data? Round the slope and y-intercept of the line to three decimal places. X=4,7,10,12,13 y= 5,7,12,14,18
Answer:
y = 1.383x - 1.526
Step-by-step explanation:
Intercept- -1.526
Slope- 1.383
Line of best fit- y = 1.383x - 1.526
Answer:
[tex]y=1.383x-1.526[/tex]
Step-by-step explanation:
The given data table is
x : 4 7 10 12 13
y : 5 7 12 14 18
We need to find the equation of the best fit line.
The general form of a best fit line is
[tex]y=mx+b[/tex] .... (1)
where, m is slope and b is y-intercept.
[tex]m=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]b=\overline{y}-b\overline{x}[/tex]
Using the graphing calculator we get
[tex]m=1.38321\approx 1.383[/tex]
[tex]b=-1.52555\approx -1.526[/tex]
Substitute m=1.383 and b=-1.526 in equation (1).
[tex]y=1.383x-1.526[/tex]
Therefore, the equation of best fit line is [tex]y=1.383x-1.526[/tex].
Yoda purchases a light saber for $1,678 with an installment loan that has an APR of 12%. The store financing requires a 15% down payment for 12 monthly payments. What is the finance charge?
Answer:$2,000
Step-by-step explanation:
Why is MAE ≅ TON
HL
HA
LL
Answer:
HL
Step-by-step explanation:
HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.
In the given right triangles MAE and TON,
AM = OT,
EM = NT,
Thus, by the HL postulate,
Δ MAE ≅ Δ TON
First option is correct.
Anthony deposited $14,000 with a bank in a 5-year certificate of deposit yielding 6% compounded daily. Find the compound amount
A) $18,897.56
B) $32,897.56
C) $17,976.05
D) $16,542.10
Answer:
Total = 14,000 * 1 + (.06 / 365) ^365*5
Total = 14,000 * 1.0.000164383561643836^1,825
Total = 14,000 * 1.3498255274
Total = 18,897.56
Step-by-step explanation:
UGH SOMEONE PLS HELP IF YOUR GOOD AT GEOMETRY
Answer: First option.
Step-by-step explanation:
Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identifyfrom the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.
You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.
Therefore, the conclusion is: The image of Y is Y'.
Anna wants to rent movies from either Service A or Service B. Service A charges $37.92 as a subscription fee with a charge of $2.18 per movie.Service B charges $33.25 as a subscription fee plus $3.55 per movie. Service B is running a special offer where the first movie is free. Given that Anna always rents at least 1 movie in a given subscription period, how many movies would she have to rent for the average cost per movie to be equal at Service A or Service B?
Answer:
6 movies
Step-by-step explanation:
:Service A
1. $37.92 +&2.18=$40.1
2. $41.1+$2.18=$42.28
3....
4....
5....
6. $48.82+$2.18=$51
Service B
1. $33.25+free movie=$33.25
2. $33.25+$3.55=$36.8
3....
4....
5....
6. $47.45+$3.55=$51
I NEED HELP
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
answer is B)
x= 85, y = 100
Answer:
D, x=100 and y=85
Step-by-step explanation:
Hello
In every convex polygon, the sum of the measure of the interior angles is given by the expression SUM = 180 ° (n - 2) where n is the number of sides
the polygon has our sides MN, NO,OP and PM, the sum of the interior angles is
[tex]sum=180(4-2)\\sum=360 degrees[/tex]
[tex]360= x +y +80+95\\360-80-95= x+y\\x+y=185[/tex]
looking at the graph it is observed that angle x° is obtuse (more than 90° but less than 180°.) and the angle y is acute (The acute angle is the small angle which is less than 90°)
so
[tex]x>y[/tex]
[tex]x+y=185[/tex]
the response option that meets these two conditions is D, x=100 and y=85
TW is a perpendicular bisector of chord QE. Identify the diameter. The answer with the red arrow is Incorrect!
Answer:
50m.
Step-by-step explanation:
When 2 chords of a circle intersect the following products are equal:
15 * 15 = 5 * (TW - 5)
5TW = 225 + 25 = 250
TW = 250/5 = 50 m
Option c 50m
What is the theorem of the chord from the center?When a line passes through the center of the circle to the chord then the line is perpendicular bisector of the same chord which means it divide the chord in equal parts and makes an angle of 90 degrees with the chord.
What is the Pythagoras theorem?Pythagoras theorem is the theorem used to calculate the hypotenuse in a right-angled triangle from the two legs of the triangle.
hypotenuse² = base²+height².
Solving the problemLet the center (the point in bold be C) and the point of intersection between QE and TW be R, So CQ is the radius, CR = radius-5.
Let the radius be 'r' so In Triangle CQR using the Pythagoras theorem
r² = (r-5)²+15²
r²-(r-5)²=225
(r-(r-5))(r+r-5) = 225
5.(2r-5)=225
(2r-5)=45
2r - 5 =45
2r=50
r = 25 and diameter is equal to 2*r and hence the diamter is 50.
The diameter in the figure is 50m
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Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).
A. y + 1 = -2(x – 5)
B. y – 1 = -2(x – 5)
C. y – 5 = -2(x + 1)
D. y -5 = -2(x – 1)
Answer:
A. y + 1 = -2(x – 5)
Step-by-step explanation:
For a line with slope m through point (h, k), the equation is ...
y -k = m(x -h)
Fill in your values of m=-2, h=5, k=-1 and you have ...
y -(-1) = -2(x -5)
y +1 = -2(x -5) . . . . . . simplify. Matches selection A.
What is the name of the thick, lower end of the digestive tract where solid waste is gathered and leaves the body?
The lower end of the digestive tract that gathers and expels solid waste from the body is called the rectum. The process involves the colon, where digestion occurs, water is reabsorbed, and waste is turned into feces, which is then eliminated through the anus.
The thick, lower end of the digestive tract where solid waste is gathered and leaves the body is called the rectum. After digested food passes through the small intestine, it enters the large intestine, or colon, where it undergoes further digestion and water reabsorption. The colon is home to a diverse microbiota that aids in digestion. The waste material, now known as feces, is then moved to the rectum. The rectum stores the feces until it triggers neural signals that lead to the urge to eliminate this waste through the anus.
Read the passage and examine the text in bold. Then, answer the question.
I always loved my grandfather's explanations of our seasons, "This is the country of three seasons. From June on to November it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress." His months were only approximate, later or earlier the rain-laden wind may drift up the water gate of the Colorado River from the Gulf and bring to us our heat, chill, or radiance. In the desert, we see the land sets its seasons by the rain.
Does the bolded portion contain an error? Choose the correction if one is needed.
a) seasons; "This is the
b) seasons: "This is the
c) seasons; however, "This is the
d) No correction needed
Answer:
The correct option is:
a) seasons; "This is the
A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.When a semicolon is used to join two or more ideas (parts) in a sentence, those ideas are then given equal position or rank.
Step-by-step explanation:
Answer:
A. seasons: "This is the
Step-by-step explanation:
What are the zeros of f(x) = (x − 7)(x − 3)(x − 2)?
For this case we must find the zeros of the following function:
[tex]f (x) = (x-7) (x-3) (x-2)[/tex]
If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:
[tex]x-7 = 0\\x = 7[/tex][tex]x-3 = 0\\x = 3[/tex][tex]x-2 = 0\\x = 2[/tex]Thus, the zeros of the function are:
7,3,2
Answer:
Option C
The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2
From the question,
We are to determine the zeros of the given function
The given function is
f(x) = (x - 7)(x - 3)(x - 2)
To determine the zeros of this function, we will set f(x) = 0
That is ,
f(x) = (x - 7)(x - 3)(x - 2) becomes
0 = (x - 7)(x - 3)(x - 2)
∴ (x - 7)(x - 3)(x - 2) = 0
Then,
We can write that
x -7 = 0 OR x - 3 = 0 OR x - 2 = 0
∴ x = 7 OR x = 3 OR x = 2
Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2
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Find the solution of this system of equations -4x-y=-18 , -7x+y=-4
Answer:
(x, y) = (2, 10)
Step-by-step explanation:
Adding the two equations will eliminate the y-variable:
(-4x -y) +(-7x +y) = (-18) +(-4)
-11x = -22 . . . . . simplify
x = 2 . . . . . . . . . divide by -11
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Put this into the first equation to find y:
-4·2 -y = -18
-8 +18 = y = 10 . . . . . add 18+y
The solution is (x, y) = (2, 10).
Answer:
x = 2 and y = 10
Step-by-step explanation:
It is given that,
-4x - y = -18 ---(1)
-7x + y= -4 ---(2)
To find the solution of equations
Step 1: Add eq(1) + eq(2)
-4x - y = -18 ---(1)
-7x + y= -4 ---(2)
-11x + 0 = -22
11x = 22
x = 22/11 = 2
Step 2: Substitute the value of x in eq (2)
-7x + y= -4 ---(2)
-7*2 + y = -4
-14 + y = -4
y = -4 + 14 = 10
Therefore x = 2 and y = 10
I need Help!!!! Please Solve and show WORK!!!
3(x+2)=15
Answer: x=3
Step-by-step explanation: First we do distributive property in the parentheses. Next we subtract both sides by 6. Lastly we divide both sides by 3. Algebraic Rules!!!
Work:
3(x+2)=15
3x+6=15
3x+6-6=15-6
3x=9
3x/3=9/3
x=3
Multiply the bracket by 3
3x+6=15
3x+6-6=15-6
3x=9
divide by 3 for 3x and 9
3x/3=9/3
x=3
Check answer by using substitution method
3(x+2)=15
3(3+2)= 15
Multiply the bracket by 3
9+6= 15
15= 15
Answer is x= 3
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