The value of the test statistic is -2.18.
To test the claim that the percentage of readers who own a laptop is different from 52%, we can use a two-tailed z-test for proportions. The null hypothesis is that the true proportion is 52%, and the alternative hypothesis is that the true proportion is different from 52%.
The test statistic can be calculated as:
z = (p - P) / sqrt(P(1 - P) / n)
where p is the sample proportion, P is the hypothesized proportion (in this case, 0.52), and n is the sample size.
Substituting the given values, we get:
z = (0.45 - 0.52) / sqrt(0.52(1 - 0.52) / 190)
z = -0.07 / 0.039
z = -1.79
The value of -1.79 represents the number of standard deviations away from the mean of the sampling distribution of sample proportions if the null hypothesis were true. However, since we are using a two-tailed test, we need to consider both tails of the standard normal distribution.
The critical value for a two-tailed test at the 0.05 level of significance is ±1.96. Since -1.79 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the correct answer is -2.18.
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(x+3)2-7. What is the degree of the function?
2
O 1
07
O 3
Answer:
7
Step-by-step explanation:
f(x) = 6 + 3 - 2
= 7
f(x) = 13 + 3 - 2
= 14
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I have a fair die with sides 1, 2, 3, 4, 5, 6. I throw the die three times. Determine the probability that the third roll is double the sum of the first two rolls.
A Basketball player shoots 16 free throws. He makes
12 and misses 4. What is the Ratio of free throws made
to total.
Explanation:
There are 12 makes and 16 total free throws.
The ratio of makes to total is 12:16. The order is important. We list the makes first, then the total second.
Divide both parts of that ratio by the GCF 4
12:16 reduces to 3:4
It means for every 3 free throws made, the basketball player has attempted 4 free throws total.
The perimeter of a rectangle is 110, and the width is 4 times
the length. What is the width?
33
044
O 66
O 55
Answer:
width = 44
Step-by-step explanation:
let l be length then width = 4l
the perimeter (P) of a rectangle is calculated as
P = 2(l + w)
given P = 110 , then
2(l + 4l) = 110 ( divide both sides by 2 )
l + 4l = 55
5l = 55 ( divide both sides by 5 )
l = 11
then
width = 4l = 4 × 11 = 44
Answer:
with = 44
Step-by-step explanation:
let the lenght l, = x
b or width = 4x
Perimeter of rectangle = 2(l + b)
110 = 2( x + 4x )
110 = 2( 5x )
110 = 10x
10x = 110
x = 110/10
x = 11
Therefore width = 4x
width = 4 (11)
with = 44
What is the value of 3x- (y / 2+ 5) when x=3.5 and y= 4?
Answer:
3.5
Step-by-step explanation:
3x -(y / 2+ 5) x = 3.5 and y = 4
= 3(3.5) -(4/2 + 5)
= 3(3.5) -(2 + 5)
= 10.5 -(2 + 5)
= 10.5 -(7)
= 10.5 - 7
= 3.5
The co-ordinates of the points P and Q are (1,-2) and (4,10) respectively. A point T divides the line PQ in the ratio 2:1. Determine the co-ordinates of T
[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(1,-2)\qquad Q(4,10)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{2:1} \\\\\\ \cfrac{P\underline{T}}{\underline{T} Q} = \cfrac{2}{1}\implies \cfrac{P}{Q} = \cfrac{2}{1}\implies 1P=2Q\implies 1(1,-2)=2(4,10)[/tex]
[tex](\stackrel{x}{1}~~,~~ \stackrel{y}{-2})=(\stackrel{x}{8}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{1 +8}}{2+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-2 +20}}{2+1} \right)} \\\\\\ T=\left( \cfrac{ 9 }{ 3 }~~,~~\cfrac{ 18}{ 3 } \right)\implies T=(3~~,~~6)[/tex]
Question 1.
What’s k^2+2k-24 factored?
Question 2.
What’s 4k^2-1 factored?
Question 3.
What’s x^2+11x+28=0 factored?
Answer:
(k+4)(k-6)
(2k+1)(2k-1)
(x+7)(x+4)=0
a lot acceptance sampling plan for large lots calls for sampling 50 items and accepting the lot if the number of nonconformances is no more than 5. showing work, find the approximate probability of acceptance if the true proportion of nonconformances in the lot is 10%
The approximate probability of acceptance if the true proportion of non conformances in the lot is 10% is 0.964
To find the approximate probability of acceptance, we can use the binomial distribution. Let's define the following variables
n = 50 (sample size)
p = 0.1 (true proportion of nonconformances in the lot)
q = 1 - p = 0.9 (true proportion of conformances in the lot)
k = 0, 1, 2, ..., 5 (number of nonconformances allowed)
The probability of accepting the lot is the probability of observing k or fewer nonconformances in a sample of size n
P(X ≤ k) = Σ [n choose i] p^i q^(n-i), i=0 to k
Using a binomial calculator or software, we can find the probability of acceptance to be
P(X ≤ 5) ≈ 0.964
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The Johnson set aside money and their budget for food for the anniversary. They spent $320 but said aside 25% of that how much did the Johnson said aside for the food party?
In the word problem, Johnson set aside $80 for food party.
What is percentage?
Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.
Here Total money that Johnson has is 100%.
In 100% of money he spent $320 and set aside 25%.
Then Money he spent = 100%-25% = 75%.
Then,
100% = 320
25% = x
=> x = [tex]\frac{320\times25\%}{100\%}[/tex] = $80.
Hence Johnson set aside $80 for food party.
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A man sold a shop and a terrace house for RM 240 000 each and sustained a loss of 25% for selling the shop and earned a profit of 25% from the terrace house. Find the amount of profit or loss.
Answer:
The amount for loss would be RM 600 and the amount for profit would be RM 600.
Step-by-step explanation:
Loss percent
25=loss/CP *100
25/100=L/CP *100
25/100=100L/240,000
10000L/10000=240,000*25/10000
L=24*25
L=RM 600
Profit percent
25/100=P/240,000 *100
25/100= 100P/240000
10000P/10000=240000*25/10000
P=RM 600
Answer:
Step-by-step explanation:
RM (≧▽≦)
Can someone please tell me the answer
The correct statement is the area of the two inner squares on the left must be the same as the area of the inner square on the right.
Define squareA square is a geometric shape with four equal sides and four right angles. It is a type of rectangle, and also a type of parallelogram. In a square, all interior angles measure 90 degrees, and the diagonals bisect each other at 90-degree angles.
there are two identical squares, each with an area of 52 square units (since each side measures 7 units). The two squares are arranged in such a way that they form a larger square with sides measuring 14 units. The area of this larger square is 142 square units.
there is also a square with sides measuring 13 units. This square has an area of 132 square units.
If we subtract the area of the two inner squares from the area of the larger square in the left figure, we get:
142 - 2(52) = 38
This means that the four triangles in the right figure must have a total area of 38 square units, which is the difference between the area of the large square (132 square units) and the area of the inner square (94 square units). Since the four triangles are congruent, each triangle must have an area of 9.5 square units.
Therefore, the area of the two inner squares on the left must be the same as the area of the inner square on the right, since they all have an area of 94 square units (which is the area of the large square minus the area of the four triangles). This leads to the relationship:
52 + 122 = 132
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For the following Isosceles Triangle, find X:
X =
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
can you help me please we must find tge measurment of area and perimeter
The area of the composite figure is 47 cm².
The perimeter of the composite figure is 36 cm.
How to find the area and perimeter of a composite figure?The figure above is a composite figure because it's compose of two shapes.
Therefore, we have to find the area of the individual shape and sum it to get the area of the composite figure.
Hence,
area of the composite figure = area of the rectangle1 + area of the rectangle2
55 mm = 5.5 cm
area of the rectangle1 = 2 × 5.5 = 11 cm²
60mm = 6 cm
l = 2 + 6 = 8cm
w = 10 - 5.5 = 4.5 cm
area of the rectangle2 = 8 × 4.5
area of the rectangle2 = 36 cm²
Therefore,
area of the composite figure = 36 + 11 = 47 cm²
perimeter of the composite figure = 2 + 10 + 8 + 4.5 + 6 + 5.5
perimeter of the composite figure = 36 cm
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suppose that three users share a 4mbps link, but each user transmits only 10 percent of the time. what is the probability that at any given time, all three users are transmitting simultaneously? (2 points) 0.1 0.001 0.4 0.064
The probability that at any given time, all three users are transmitting simultaneously is option (b) 0.001
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
The question asks about the probability of all three users transmitting simultaneously on a shared 4Mbps link, given that each user transmits only 10% of the time.
Assuming that the transmission of each user is independent of the others, the probability of all three users transmitting simultaneously can be calculated using the binomial distribution as follows
P(all three transmitting) = (0.1)^3 = 0.001
Therefore, the correct option is (b) 0.001
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What is the value of x?
Answer: x = 27
Step-by-step explanation:
we know that vertical angles are equal to each other, so
4x + 7 = [ 5 (x - 4) ]
distribute
4x + 7 = 5x - 20
subtract 4x from each side to combine variables
4x - 4x + 7 = 5x - 4x - 20
simplify
7 = x - 20
add 20 to both sides to solve for x
7 + 20 = x -20 + 20
simplify
27 = x
check your work, substitute value of x into equation
4x + 7 = 5x - 20
4(27) + 7 = 5(27) - 20
108 + 7 = 135 - 20
115 = 115
solution equals and is true, problem solved!
Question 7 (Multiple Choice Worth 2 points)
(Equivalent Algebraic Expressions MC)
Which is an equivalent expression for
d1¹2
2
11d¹2
2
11d
00.2d¹2
4d-³
22d⁹
?
According to the given information, option (b) is the correct answer.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent quantities or values that can vary, depending on the values assigned to the variables in the expression. Algebraic expressions can be simple or complex, and they can have one or more variables.
b) 2/11d¹² is the equivalent expression for 4d⁻³ /22d⁹.
To simplify the expression, we can use the rule of negative exponents: d⁻ⁿ = 1/dⁿ
So, 4d⁻³ /22d⁹ = 4/22d¹² = 2/11d¹²
Therefore, option (b) is the correct answer.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each hypotenuse length with the leg lengths that will create a right triangle.
Hypotenuse
√6 units
√5 units
√8 units
√3 units
√5 units, √3 units
Legs
√1 unit, √2 units
√2 units, √3 units
√5 units, √3 units
√5 units, 2 units
√5 units, 1 unit
the completed pairs are - √5 units, 2 units
Starting with the first pair, we have √5 units on both tiles, so we can place them in the same box.
Moving on to the second pair, we have √3 units on one tile and √5 units on the other. We need to find a pair that matches √3 units. Since there is no tile with √3 units, we cannot place this pair in the same box.
Lastly, we have two tiles left - one with √5 units and another with 1 unit. We need to find a pair that matches 1 unit. Since there is no tile with 1 unit, we cannot place this pair in the same box either.
Therefore, the completed pairs are:
- √5 units, √5 units
- √5 units, 2 units
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The table shows the possible outcomes of spinning the given spinner and tossing a fair coin. Find the probability of spinning a 1 and tossing a head
Considering a six-sided spinner, it is found that the probability of spinning a 1 and tossing a head is of [tex]\dfrac{1}{12}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
For the spinner, one is one out of six possible outcomes.For the coin, a head is one out of two possible outcomes.Since the events are independent, the probability of spinning a 1 and tossing a head is given by:
[tex]\text{p}=\dfrac{1}{6} \times\dfrac{1}{2} =\dfrac{1}{12}[/tex]
The scale on the map is 1:25000
How many kilometres on the ground is represented by 6cm on the map?
Answer: 150,000 km
Step-by-step explanation: If every centimeter is equal to 25000 kilometers, than 6 x 25000 = 150,000.
Answer:
1.5 km
Step-by-step explanation:
1 kilometer = 1000 meters and 1 meter = 100 cm, so 1 km = 100,000cm
If the scale on the map is 1:25,000, 6cm on the map = 150,000 cm
Since 1 km = 100,000 cm, 1 km/100,000 cm = 1
150,000 cm x 1 km/100,000 cm = 1.5 x 1km = 1.5 km
Clare thinks knowing the measures of 2 angles is enough to show triangle similarity. Do you agree?
1. yes
2. no
Explain your reasoning.
Answer:
yes this is because to find similarity of triangles two interior angles must be the same which automatically means that the lat angle would be the same
Wendell wants to make a wooden lid for a decorative box.
The lid needs to be 6 1/2inches wide and 8 1/2inches long with sides 2 inches deep.
Tο make a wοοden lid fοr a decοrative bοx with the given dimensiοns, yοu will need tο cut a rectangular piece οf wοοd with dimensiοns 10 1/2 inches by 12 1/2 inches. This will allοw fοr the 2 inch deep sides tο be added tο the lid.
What is area?In a twο-dimensiοnal space, area is a unit used tο describe hοw big a surface οr regiοn is. It is measured in terms οf square measurements like square inches (in2), square metres (m2), οr square feet (ft2). A shape's area can be calculated using a variety οf fοrmulas, including multiplying the shape's length by its breadth.
The area οf a rectangle, fοr instance, can be calculated using the fοrmula A = l w, where A denοtes the area and l, w, and w are the length and breadth respectively. Geοmetry, physics, architecture, and building are just a few οf the fields in which the cοncept οf area is applied.
Tο calculate the dimensiοns οf the rectangular piece οf wοοd needed fοr the lid, yοu need tο add twice the depth οf the sides (2 inches) tο each οf the width and length οf the lid:
Width οf wοοden lid = 6 1/2 inches + 2 inches + 2 inches = 10 1/2 inches
Length οf wοοden lid = 8 1/2 inches + 2 inches + 2 inches = 12 1/2 inches
Therefοre, the rectangular piece οf wοοd needed fοr the lid shοuld be 10 1/2 inches by 12 1/2 inches.
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Complete Question:
Wendell wants to make a wooden lid for a decorative box.
The lid needs to be 6 1/2inches wide and 8 1/2inches long with sides 2 inches deep.
Part A
Find the area of wood that Wendell will need to make the lid.
Drag numbers to complete the measurements.
Each tile may be used once or not at all.
The triangles are similar.
Answer:
AC = 16 units
Step-by-step explanation:
we can solve with an equation to find the value of x and then add 1 to find AC (work in attached drawing).
Here is a graph of the equation 2x-y=1 are the points (0,1/2) and (-7,-3) solutions to the equation 
HELPPPP ASAP
Neither of the two points is a solution of the linear equation.
Are the points solutions of the linear equation?Here we have the linear equation.
2x - y = 1
And we have the graph of this line.
We want to check if the points (0, 1/2) and (-7, -3) are solutions.
You can do this in two ways, one is finding the points on the coordinate axis and check if the points lie on the line, the other is replace the values in the eequation and see if it becomes true.
Because the graph is really small in the image, I will do the second one.
For (0, 1/2) we have:
2*0 - 1/2 = 1
0 - 1/2 = 1
-1/2 = 1
This is false.
For the second (-7, -3) we have:
2*-7 - (-3) = 1
-14 + 3 = 1
-11 = 1
This is false.
Neither of the points is on the line.
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What is the solution set of this system of equations?
y = -x^2 + 2x + 4
x + y = 4
A. (7, -3) and (4, 0)
B. ( 7, -3) and (0, 4)
C. (0, 4) and (4, 0)
D. (0, 4) and (3, 1)
The solution set of this system of equations (C) (0, 4) and (4, 0).
Define simultaneous equationSimultaneous equations refer to a set of two or more equations that need to be solved together to determine the values of the variables that satisfy all the equations.
Given:
y = -x²+ 2x + 4
x + y = 4
We can substitute the first equation into the second equation to get:
x + (-x² + 2x + 4) = 4
Simplifying, we get:
-x² + 3x = 0
Factorizing, we get:
x(-x + 3) = 0
So the possible values of x are x = 0 and x = 3.
If x = 0, then y = 4 (from the second equation).
If x = 3, then y = -3 (using the first equation).
Therefore, the solution set of the system of equations is (0, 4) and (3, -3).
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Use point-slope form to write the equation of a line that passes through the point
(2,8) with slope - 1/3
Answer:
[tex]y - 8 = - \frac{1}{3} (x - 2)[/tex]
The cylinder shown has a diameter of 20 in. and a height of 4 in.
20 in.
Use 3.14 for T.
What is the approximate volume of the cylinder?
OA. 251.2 in.3
OB. 502.4 in.³
OC. 879.2 in.3
OD. 1,256 in.3
OE. 5,024 in.3
4 in.
Answer:
1256 in.3
Step-by-step explanation:
V = pi x r^2 x h
V = 3.14 x 20/2 x 4
V = 3.14 x 10 x 4
V = 1256in^3
Answer:
1256 in³
Step-by-step explanation:
To calculate volume of a cylinder the formula is: π · r2 · h
Since Pi is already given to us as 3.14, we now have to find the radius
The radius is always the diameter cut in half meaning it will be 20/2 which gives us 10 (radius is figured)
The height is given to us as 4 meaning the equation will be
3.14 x 10 x 10(seeing as it's radius squared) x 4
10x10 = 100
100 x 4 = 400
400 x 3.14 = 1256
The answer is in cubed(³) because it is volume
A similar shape will have sides that are "in proportion". The width of a rectangle is 12 cm and the width of a similar rectangle is 6000 mm.
What is the length of the larger rectangle if the length of the smaller rectangle is 15 cm?
Determine the scale factor used to enlarge the smaller rectangle.
What is the relationship between the areas of the two rectangles?
According to the question the area of the smaller rectangle is 0.04 times the area of the larger rectangle.
Explain Area?The surface area of an object is the sum of all the shapes that make up its surface. This kind of rectangle's area is calculated by multiplying its length and breadth.
Given,
To solve this problem, we first need to find the length of the larger rectangle, which we can do using the fact that the two rectangles are similar, meaning their corresponding sides are in proportion.
We can set up a proportion using the widths of the two rectangles:
12 cm / 15 cm = 6000 mm / x
where x is the length of the larger rectangle in millimeters.
We could cross-multiply and simplify to find x's value:
12 cm * x = 15 cm * 6000 mm
x = (15 cm * 6000 mm) / 12 cm
x = 7500 mm
So the length of the larger rectangle is 7500 mm.
To determine the scale factor used to enlarge the smaller rectangle, we can divide the corresponding sides of the two rectangles. Since we know the width of the smaller rectangle is 12 cm and the width of the larger rectangle is 6000 mm (which is equivalent to 60 cm), we can set up the proportion:
12 cm / 60 cm = 1/5
So the scale factor used to enlarge the smaller rectangle is 1/5 or 0.2.
Finally, we can find the relationship between the areas of the two rectangles by using the fact that the ratio of the areas of two similar shapes is equal to the square of the scale factor. In this case, the scale factor is 0.2, so:
Area of smaller rectangle / Area of larger rectangle = (0.2)^2
Area of smaller rectangle / Area of larger rectangle = 0.04
Therefore, the area of the smaller rectangle is 0.04 times the area of the larger rectangle.
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The science team is creating a float for the homecoming parade. They want to make a rocket ship by using foam to create a cone that is stacked on top of a cylinder. The bases of the cylinder and cone will be congruent and have a radius of 1.5 feet. The height of the cylinder will be 4 feet, and the height of the cone will be 2 feet. If all the visible surfaces of the structure need to be painted except for the bottom of the cylinder, then what area needs to be painted? Round your answer to the nearest tenth of a square foot.
Therefore, approximately 65.9 square feet of paint will be needed to cover all visible surfaces of the rocket ship float.
What is surface area?Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.
by the question.
To calculate the total surface area that needs to be painted, we need to find the surface area of the cylinder and the surface area of the cone, and then add them together.
Surface area of the cylinder:
The cylinder has a radius of 1.5 feet and a height of 4 feet. The formula for the surface area of a cylinder is:
[tex]SA_cylinder = 2πrh + 2πr^2[/tex]
where r is the radius and h is the height of the cylinder.
Plugging in the values, we get:
[tex]SA_cylinder = 2π(1.5)(4) + 2π(1.5)^2\\SA_cylinder = 12π + 4.5π\\SA_cylinder = 16.5π[/tex]
[tex]SA_cylinder = 51.8 ft²[/tex] (rounded to the nearest tenth)
Surface area of the cone:
The cone also has a radius of 1.5 feet, and a height of 2 feet. The formula for the surface area of a cone is:
[tex]SA_cone = πr√(r^2 + h^2)[/tex]
Plugging in the values, we get:
[tex]SA_cone = π(1.5)√(1.5^2 + 2^2)\\SA_cone = π(1.5)√(2.25 + 4)\\SA_cone = π(1.5)√6.25[/tex]
[tex]SA_cone = π(1.5)√(1.5^2 + 2^2)\\SA_cone = π(1.5)√(2.25 + 4)\\SA_cone = π(1.5)√6.25[/tex] (rounded to the nearest tenth)
Total surface area:
Adding the surface area of the cylinder and the surface area of the cone, we get:
[tex]Total SA = SA_cylinder + SA_cone[/tex]
Total SA ≈ 65.9 ft² (rounded to the nearest tenth)
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Rounded to the nearest tenth of a square foot, the area that needs to be painted is 76.9 square feet.
What exactly is a cylinder?
In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance.
The first step is to calculate the lateral surface area of the cylinder and cone. The lateral surface area of the cylinder is the product of the height and the circumference of the base, which is:
4 feet x 2π(1.5 feet) = 12π square feet
The lateral surface area of the cone is half the product of the slant height and the circumference of the base, which is:
1/2 x 2π(1.5 feet) x √(2^2 + 1.5^2) = 7.5π square feet
The total area to be painted is the sum of the lateral surface areas of the cylinder and cone, plus the area of the base of the cone, which is congruent to the base of the cylinder. The base has a radius of 1.5 feet, so the area of each base is:
π(1.5 feet)^2 = 2.25π square feet
The total area to be painted is:
12π + 7.5π + 2(2.25π) = 24.5π square feet
Using a calculator, this is approximately equal to 76.95 square feet.
Therefore, Rounded to the nearest tenth of a square foot, the area that needs to be painted is 76.9 square feet.
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The perimeter of a rectangle is 20cm and its area is 24 cm^2. calculate the length and width of the rectangle.
using quadractic equation.
Answer:
see explanation
Step-by-step explanation:
let length be l and width be w , then perimeter P is
P = 2(l + w)
given P = 20 , then
2(l + w) = 20 ( divide both sides by 2 )
l + w = 10 ( subtract w from both sides )
l = 10 - w → (1)
area (A) is calculated as
A = lw
given A = 24 , then
lw = 24
substitute l = 10 - w into this equation
(10 - w)w = 24
10w - w² = 24 ( subtract 24 from both sides )
10w - w² - 24 = 0 ( multiply through by - 1 and rearrange )
w² - 10w + 24 = 0 ← in standard form
(w - 4)(w - 6) = 0 ← in factored form
equate each factor to zero and solve for w
w - 4 = 0 ⇒ w = 4
w - 6 = 0 ⇒ w = 6
substitute these values into (1)
w = 4 : l = 10 - 4 = 6
w = 6 : l = 10 - 6 = 4
Then
length = 6 cm , width = 4 cm
or
length = 4 cm , width = 6 cm
graph the equation y=xpower2 + 10x + 21 on the accompanying set of axes. you must plot the roots and the vertex
The graph of [tex]y=x^2+10x+21[/tex] includes a vertex at (-5, 17) and two roots at (-6, 0) and (-4, 0).
To graph the equation [tex]y=x^2+10x+21[/tex], we can complete the square to find the vertex and use the quadratic formula to find the roots.
First, we'll find the vertex. We can do this by adding and subtracting [tex](10/2)^2 = 25[/tex] inside the parentheses:
[tex]y = x^2 + 10x + 21[/tex]
[tex]y = (x^2 + 10x + 25) - 4 + 21[/tex]
[tex]y = (x + 5)^2 + 17[/tex]
So the vertex is (-5, 17).
Next, we'll find the roots using the quadratic formula:
x = (-b ± sqrt([tex]b^2 - 4ac[/tex]))/(2a)
where a = 1, b = 10, and c = 21.
x = (-10 ± sqrt([tex]10^2 - 4[/tex](1)(21)))/(2(1))
x = (-10 ± sqrt(4))/(2)
x = -5 ± 1
So the roots are x = -6 and x = -4.
Now we can plot the vertex at (-5, 17) and the roots at (-6, 0) and (-4, 0) on the accompanying set of axes.
To learn more about vertex please click on below link
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