The measure of the ∠1 for the given angles of the triangle are found as 1162/13.
Explain the angle sum property of the triangle?The internal angle of a triangle is just the angle formed by two of its sides. It is often referred to as the triangle's interior angle property. Because of this characteristic, a triangle's interior angles add up to 180 degrees.The given angles are-
∠1 = 7x - 7.
∠2 = 4x + 2
∠3 = 2x + 6
By the angle sum property of the triangle.
∠1 + ∠2 + ∠3 = 180
Thus,
7x - 7 + 4x + 2 + 2x + 6 = 180
Simplifying,
13x = 179
x = 179/13
So, ∠1 becomes-
∠1 = 7x - 7
∠1 = 7(179/13)- 7
∠1 = 1162/13
Thus, the measure of the ∠1 for the given angles of the triangle are found as 1162/13.
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my last try anone willing to help
Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as 4 = 3x ⁽ˣ⁺²⁾
Which property of log function is used?
The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.
These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.
A log function can be written in exponential form using
logₐ m = x ⇒ m = ax
According to the given question:
The given logarithmic function is
log₍ₓ₊₂₎(4) = 3x
On applying the property we get
4 = 3x ⁽ˣ⁺²⁾
Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾
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which is the inverse of graph f
Answer: the one in blue
Step-by-step explanation:
A juice company introduces a new recipe which
contains less sugar. A bottle of juice made using the
new recipe is shown below.
If the bottle of juice now contains 8.19 g of sugar,
how many grams (g) of sugar did it contain before
the new recipe was introduced?
Answer: x = 18
Step-by-step explanation:
1) 100% - 54.5% = 45.5%.
2) 45.5/100 = 0.455.
3) 0.455 * X = 8.19g.
4) x = 8.19/0.455.
5) x = 18.
a fair coin is flipped 10 times and the number of heads is counted. this procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. which of the frequency tables below is most likely to contain the results from these 100 trials?
This table illustrates how many trials out of 100 resulted in each number of heads out of ten flips. Because it precisely depicts the possibility of each occurrence, this frequency table is the most likely to include the outcomes of the 100 trials.
The likelihood of receiving any number of heads out of ten flips is the same in a fair coin flip, therefore the table should show a fairly uniform distribution of trials across each number of heads. Overall, the frequency table most likely to capture the outcomes of the 100 trials has the number of heads out of 10 flips as rows and the number of trials out of 100 as columns.
This table may be used to precisely depict the data as well as determine the likelihood of each occurrence.
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please help meeeeeeeeeeeeeeeeeee
Answer:
6, 7, 10
Step-by-step explanation:
7 > x - 4 ( add 4 to both sides )
11 > x , then
x < 11
the values from the table which are solutions are 6, 7, 10
Answer:
Answer is 11
Step-by-step explanation:
7+4>z-4+4
11>z
Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.
What does z score mean?An indicator of how nearly a value relates to the mean of either a set of values is called a Z-score.Z-score is quantified using standard deviations relative to the mean.The data point's entire score is equal to the mean score when the Z-score is 0.The amount that the raw score departs first from mean is determined using the Z score.These steps are used to determine the Z score:
z = (x - μ)/σ
As mentioned in question-
x > 550 and μ = 500, σ = 40:
z = 550 - 500 / 40
z = 1.25
Obtain the p-value from normal distribution chart,
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.
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Write the point-slope form of the equation of the line that goes through the points (-5, -5) and (1, -3).
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]
a vertical cylinder is leaking water at a rate of ft3/sec. if the cylinder has a height of ft and a radius of ft, at what rate is the height of the water changing when the height is ft?
The rate in the height of water changing for the given cylinder is equal to 0.318m/s.
As given in the question,
Change in volume represent the decrease in rate of change of water height in the cylinder in time t
dV/dt = 4m³/sec.
Decrease in volume represent the change in the height of the water
Let 'h' be the height
h = 10m
radius 'r' = 2m
V = πr²h
Rate of change of leaking water only change the height radius remain constant.
⇒V = (3.14)(2²) h
Differentiate both the side with respect to 't' to get the rate of change
dV/dt = (3.14)(4)dh/dt
⇒4 =(3.14)(4)dh/dt
⇒dh/dt = 4/ (3.14)(4)
⇒dh/dt = 0.318 m/s
Therefore, the rate of change of height is equal to 0.318m/s.
The complete question is:
A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?
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how many such tests would it take for the probability of committing at least one type i error to be at least 0.7? (round your answer up to the next whole number.)
The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118 .
In the question ,
it is given that ,
the probability of committing at least , type I error is = 0.7
we have to find the number of tests ,
let the number of test be n ,
the above mentioned situation can be written as
1 - P(no type I error is committed) ≥ P(at least type I error is committed)
which is written as ,
1 - (1 - 0.01)ⁿ ≥ 0.7
-(0.99)ⁿ ≥ 0.7 - 1
(0.99)ⁿ ≤ 0.3
On further simplification ,
we get ,
n ≈ 118 .
Therefore , the number of tests are 118 .
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on average, a banana will last 6.5 days from the time it is purchased in the store to the time it is too rotten to eat. is the mean time to spoil greater if the banana is hung from the ceiling? the data show results of an experiment with 15 bananas that are hung from the ceiling. assume that that distribution of the population is normal.
No, the mean time to spoil is not necessarily greater if the banana is hung from the ceiling.
This can only be determined by analyzing the data from the experiment with 15 bananas. If the sample mean is greater than 6.5 days, then the mean time to spoil is greater when the banana is hung from the ceiling. If the sample mean is less than or equal to 6.5 days, then the mean time to spoil is not necessarily greater when the banana is hung from the ceiling.
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Eating Together. In December of 2001, 38% of adults with children under the age of 18 reported
that their family ate dinner together seven nights a week. In a recent poll, 403 of 1122 adults
with children under the age of 18 reported that their family ate dinner together seven nights a
week. Has the proportion of families with children under the age of 18 who age dinner together
seven nights a week decreased? To answer this question, conduct a hypothesis test using the
a = 0. 05 level of significance. Round values for the sample proportion and p-value to three
decimal places
Fewer families with kids under 18 now have dinner together seven nights a week
Given,
Let p represent the percentage of households with kids under 18 that have supper together every night.
So, Null Hypothesis, : p 38% (meaning that more or the same number of families with children under the age of 18 now have dinner together seven nights a week.)
Alternate Hypothesis, : p < 38% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = ~ N(0,1)
Where,
p = sample proportion of families = 403/1122 = 0.36
n = sample of adults with children under the age of 18 = 1122
So,
The test statistics = -1.32
The value of z-statistics is -1.32.
Also, the P-value of the test statistics is given by;
P-value = P(Z < -1.32) = 1 - P(Z 1.32)
= 1 - 0.9066 = 0.0934
We have enough data to reject our null hypothesis since the test statistics will fall in the rejection region because the P-value for our test statistics is less than the level of significance, which in this case is 0.0934 < 0.10.
As a result, we draw the conclusion that fewer families with children under the age of 18 now have supper together seven nights a week.
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im almost done with this
Answer:
[tex]1\frac{1}{2}[/tex]
Step-by-step explanation:
we multiply the fractions
1/8 x 12/1
12/8
1 4/8
1 1/2
Hopes this helps please mark brainliest
a piece of solid aluminum is in the shape of a cube. if the temperature of the cube is increased so that the length of each side increases by a factor of 0.001 (that is, by 0.10%), by what factor does the volume of the cube increase?
The factor by which the volume of cube increased is 0.0030
What is a cube ?
A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.
The fundamental distinction between a cube and a square is that the former has three dimensions—length, breadth, and height—while the latter only has two. A cube is composed of squares, which are a type of 2-dimensional (2D) shape (such as a circle, square, triangle, etc.).
let l be the side of a cube
the new length of cube is l' = 1.001l
Initial volume (v1) = l³
final volume (v2) = (1.001)³l³
The factor by which the volume increased is = v1 / v2
= ((1.001)³l³ - l³)/l³
= 0.003003
= 3 x 0.001
≅ 0.0030
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Please HELPPPP
Quadrilateral ABCD is a square and the length of AC is 20 cm. What is the length of DE and DC?
What is
m ADE ?
For the square on the diagram, we can see that:
DE = 10cmDC = 14.14cmmADE = 45°What is the length of DE and DC?
Remember that all the sides of a square have the same length.
Here we know that AC, the diagonal of the square, has a measure of 20 cm.
Then the length of DE, which is half of the diagonal of the square, is half of that, then:
20cm/2 = 10cm
DE = 10cm
DC is one of the sides of the square. Remember that for a square of sidelength S, the diagonal is:
D = √2*S
Then the sidelength is:
S = D/√2
Here we know that the diagonal measures 20 cm, then:
DC = S = 20cm/√2 = 14.14 cm
DC = 14.14cm
Finally, mADE refers to the measure located at the vertex D on the triangle on the angle ADE.
Remember that all the angles of a square measure 90°, and here the ray DE divides that angle in two halves, then mADE = 90°/2 = 45°
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john computes the sum of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$. what is the sum of these 15 sums?
Sum of the 15 two elements subset of $\{1,2,3,4,5,6} = ( N-1) (N)(N+1)/2
Three elements....two at time (1,2) (1,3) (2,3)....sum = 12
Four elements .... two at a time (1,2) (1,3) (1,4) (2,3) (2,4) (3,4) .....sum = 30
Five elements....two at a time (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)
Note that for N elements taken 2 at a time....the pattern of sums seems to be
= (N-1)(N)(N+1) / 2
For taking 6 elements taking 2 at a time the sum should be
=(5)(6)(7) /2
=210 /2
=105
Therefore, total sum of those 15 sums of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$ = 105
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I NEED HELP PLEASE WITH THIS PROBLEM
Answer:
48
Step-by-step explanation:
the ratio of blue cards to yellow cards can be expressed with
4:3.
the total amount of blue and yellow cards can be interpreted as 4x+3x=7x
then you can find the value of x by dividing 84/7, which is 12
since the value of blue cards is 4x, 4(12) = 48
how many ways are there to arrange the letters in the word mississippi so that either all the is are consecutive or
The required number of ways to arrange the letters in the word mississippi so that either all the is are consecutive are 11!/4!2!4!..
What is factorial?factorial, in science, the result of all certain whole numbers not exactly or equivalent to a given positive whole number and meant by that whole number and an interjection point. Subsequently, factorial seven is composed 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is characterized as equivalent to 1.
According to question:We have,
All out no. of words = 11
Had all letters been unmistakable, the response would have been =11!. However, as it isn't the case we want a method for diminishing it to consider the way that a portion of its letter sets are same.
In each game plan of the expressions of "mississippi" :
There are 4 S's which can be improved in 4! ways.Same thing with the I's , andTwo P's which can be improved in 2! waysPresently taking into truth the over three focuses decrease 11! by separating it by 4!2!4! also, you have your response.
Thus, required arrangement is 11!/4!2!4!.
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a population of protozoa develops with a constant relative growth rate of 0.6685 per member per day. on day zero the population consists of two members. find the population size after seven days. (round your answer to the nearest whole number.)
When the population of a protozoa develops with a constant relative growth rate of 0.6685 per member per day, and there are two members on the day zero, the population after will consist of 7 at the end of seven days period.
The total population of the protozoa at the end of the seven days can be computed using the calculations given below,
Total Population = Growth Rate x Number of Days + Day zero Population
Total Population = (0.6685 x 7) + 2
Total Population = 6.667, or ~ 7.
Therefore, there will be 7 protozoa at the end of seven days.
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A cylindrical container with capacity 355cc is to be produced. The bottom and side of the container are to be made of material that costs 0. 02 cents per cm2 , while the top of the container is made of material costing 0. 03 cents per cm2. Find the dimensions that will minimize the cost of the container. Provide a convincing argument that your results give the least expensive cost
The dimension of the cylindrical container that will minimize the cost of the container is a radius of 4.371 and a height of 25.85
since we know that the volume of a cylinder is :
355=πr²h, where r is the radius of the base and h is the height
So, we can say h=355/πr², here we have two circular components with the areas 2A=2πr² , for the cost of 0. 02 cents per cm² and a rectangular component of area A=2πrh , with cost of 0. 03 cents per cm².So the cost function will be :
C=0.02(2πr²)+0.03(2πrh)
C=0.04(πr²)+0.06(πrh), substuting the vale of h
C=0.04(πr²)+0.06(πr(350/πr²))
C=0.04(πr²)+(21/r), differentiating both sides we get .
C'=0
=>0.08(πr)-(21/r²)= 0, simplifying the equation we get
=>r= 3√525/2π =4.371
so for h, it will be: 355/π(3√(525/2π)) = 355/π(3√(83.55)) =350/π( 4.371) =25.85
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a standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 1313 cards (ace, two through ten, jack, queen, and king) for a total of 5252 cards in all. 1) how many cards in the deck are either a jack or a heart?
The number of cards in the deck are either a jack or a heart are 17.
What is card deck?
A playing card is a specially made piece of card stock, heavy paper, thin cardboard, paper coated with plastic, cotton-paper blend, or thin plastic that is imprinted with distinctive motifs. To make handling easier, each card frequently has a finish on the front and back.
Given:
A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.
We have to find the number of cards in the deck are either a jack or a heart.
Since, there are four Jack in a 52 card deck.
So, one jack can be chosen by 4C1 ways.
Also there are 13 cards of hearts in a 52 card deck.
So, one heart can be chosen by 13C1 ways.
The number of ways = 4C1 + 13C1 = 4 + 13 = 17.
Hence, the number of cards in the deck are either a jack or a heart are 17.
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1. -2x² = -72
2. x² + 8 = -41
3. (2y - 3)² = 49
4. 4y² - 80 = 0
[ Solve the following quadratic Equations by extracting the square roots.] with solutions you can write in on paper:)
Please help me with this question with solution ??
The measure of the value of [x] is x = √5/2
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle as shown in the image.
We can write -
sin(30) = x/(√5)
x = √5 sin (30)
x = √5/2
Therefore, the measure of the value of [x] is x = √5/2.
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Evaluate each expression.
Answer:
0.2
Step-by-step explanation:
First part yields 0.008 if you take sqrt((1/25)^3).
Then the cuberoot of 0.008 is 0.2.
Answer:
Look at the attachment! :D
Hope this helps!
Step-by-step explanation:
a researcher found that a cigarette smoker smokes on average 31 cigarettes a day. she feels that this average is too high. she selected a random sample of 8 smokers and found that the mean number of cigarettes they smoked per day was 28. the sample standard deviation was 2.9. at
At 0.01 significance level the hypothesis is rejected.
Null Hypothesis (H₀): The sample data occurs purely from chance.
Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.
If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.
Given that,
x = 28
s = 2.9
μ = 31
n = 8
α = 0.01
Then, the Null Hypothesis : H₀ = 31
The Alternate Hypothesis : H₁ < 31
The average number of cigeratte smoker per day is less than 31.
Test Statistics:
t = x -μ / s√n
= 28 - 31/ 2.9√8
= -3/ 8.41
= -0.356
Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.
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Which tatement are true about the line of ymmetry of a regular pentagon? Select three option
The correct option for the lines of symmetry of a regular pentagon-
C: Every line bisects a vertex angle.D: Every line bisects a side.E: Every line is perpendicular to a side.Explain the term regular pentagon?When a form can be folded or the folded portion sits perfectly on top so that all other edges match when the perpendicular line goes through at one vertex to the center of one side, the shape has a line of symmetry.Now that we have established what a line of symmetry is, we can infer that a pentagon has five sides and, thus, five lines of symmetry.An image of a pentagon's five lines of symmetry is included below.
We can observe from the following photo that the lines for symmetry cut through a vertex angle, a side, and are perpendicular to either a side.
Options C, D, and E are the appropriate choices.
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Complete question is;
Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.
A) Every line connects two vertices.
B) Every line connects the midpoints of 2 sides.
C) Every line bisects a vertex angle.
D) Every line bisects a side.
E) Every line is perpendicular to a side.
Which congruency theorem can be used to prove that △ghl ≅ △khj? sss asa sas aas
We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.
We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).
According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.
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Draw a picture to show why this equation is true:
3/8 = 3 ÷ 8
Answer:
You can draw a picture like this:
Step-by-step explanation:
If we are working with fractions, then think of it as a circle.
3 circles divided by 8 people
(Draw 3 circles divided into eighths)
Now, on the first circle, write the number one into one of the slices.
Do the same to the second circle.
Now the third.
How many slices have the number 1 in it?
3 slices have the number 1 in it.
And each whole circle has 8 pieces.
3 (slices) divided by 8 (People) = 3/8
in a recent poll, 330 people were asked if they liked dogs, and 73% said they did. find the margin of error of this poll, at the 95% confidence level.
The confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,
±31.06.
On Subtracting 1 from your sample size, we get
330 – 1 = 229.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 229 and α = 0.025
from the table at df = 999 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
150 / √(330) = 1.37
Now, 2.262 × 1.37 = 31.06
So, the confidence interval be,
(150 - 31.06 , 150 + 31.06) = (138.94 , 181.06)
Hence, the confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,
±31.06.
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Mr. Jones bought 6 and 2/7 lb. of salmon. He cooked 1/5 of it for lunch. How much salmon did he have for lunch?
The amount of the salmon left after Mr Jones used some part is
5 and 1/35 lbHow to find the amount leftTotal amount of salmon bought is 6 and 2/7 lb = 6 2/7 lb
The amount used is 1/5 of the amount Mr Jones bought
= 1/5 * 6 2/7
= 44 / 35
= 1 9/35
= 1.257
The amount left is calculated by subtraction
= 6 2/7 - 1 9/35
= 176 / 35
= 5 1/35
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Find the roots of each equation x^2 - 7x + 12 = 0
Answer:
x=3,x=4
Step-by-step explanation:
(x-3)(x-4)=0
x=3, 4
Answer:
x = 3
x = 4
Step-by-step explanation:
"find the roots" means to find the solutions to the equation.
Roots are solutions are zeros are x-intercepts.
You are being asked to solve the equation.
First, factor the quadratic.
x^2 -7x + 12 = 0
(x - 3)(x - 4) = 0
This works because -3 × -4 is 12 and
-3 + -4 is -7
You see the 12 in the equation is the constant and the -7 is the middle term, the x-term in the trinomial.
So we have
(x - 3)(x - 4) = 0
Separate the two factors into two separate tiny, one-step equations.
x - 3 = 0 , x - 4 = 0
Solve.
x = 3 , x = 4
These are the roots (solutions, zeros and x-intercepts)