a line passes through point (2,-6) and has a slope of -9. write an equation in ax+by=c form for this line. use integers for a,b, and c.
// lol please help :,) //
Answer:
9x +y = 12
Step-by-step explanation:
You want the standard form equation for the line with slope -9 through the point (2, -6).
Point-slope formThe point-slope form equation is a good place to start when given a point and a slope. That equation is ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y -(-6) = -9(x -2) . . . . line with slope -9 through point (2, -6)
Standard formThis can be rearranged to the desired form:
y +6 = -9x +18 . . . . . . eliminate parentheses
9x +y = 12 . . . . . . . . add 9x -6
write a logarithmic equation (using only real numbers) that has no real solutions. explain why there are no real solutions.
The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.
This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.
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Find the number that makes the ratio equivalent to 6:1.
?:10
Answer:
60
Step-by-step explanation:
?=60, multiply each side of the ratio by 10 to get the answer
6×10:1×10
60:10
What is the approximate value of y − x? 4.9° 6.2° 11.1° 17.2°
Answer:
Step-by-step explanation:
11.1
The approximate value of y - x is 17.2°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given a right triangle LMN.
Using the tangent function,
tan (y) = 19.1 / 14.1
= 1.3546
y = tan⁻¹ (1.3546) = 53.56°
We know that,
x + y = 90°, since the other angle is 90°.
x = 90 - 53.56° = 36.44°
y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°
Hence the value of y - x is 17.2°.
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the average iq test scores of an srs of 31 seventh-grade girls in a midwest school district is 105.84. suppose that the standard deviation of iq scores in this population is known to be 15. iq scores in a broad population are supposed to have mean of 100. is there evidence that the mean in this district di ers from 100? use signi cance level
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
X = 89 represent the mean of seventh-grade girls in Midwest school district
s = 15 represent the standard deviation for the sample
n = 31 sample size
μ = 100 represent the value that we want to test
'a' represent the significance level for the hypothesis test.
't' would represent the statistic (variable of interest)
[tex]p_{v}[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses,
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis: μ = 100
Alternative hypothesis: μ ≠ 100
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] ) (Equation-1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]
t = -4.08
Calculate the P-value
First we need to calculate the degrees of freedom given by:
[tex]df = n-1[/tex]
[tex]df = 31 -1[/tex]
[tex]df = 30[/tex]
Since is a two tailed test the p value would be:
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )
[tex]p_{v}[/tex] = 0.00031
Therefore,
If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.
[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031
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a dark eyed man marries a dark eyed woman, but they have a blue eyed child. what is the probability that their second child will have blue eyes?
The probability that their second child will have blue eyes is 1/4.
Here dark eye is dominant trait and blue eyes is recessive trait.
So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.
Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).
So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.
Hence we get the required answer.
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1 point
Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales
of soft drinks and hot dogs?
The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220 * 2
How to determine the calculation that will give the closest estimateFrom the question, we have the following parameters that can be used in our computation:
Time = one week
Number of cans = 362
Unit price of soft drink = $1.75
Number of hot dogs = 221
Unit price of hot dogs = $2.35
The calculation that will give the closest estimate is represented as
Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs
Substitute the known values in the above equation, so, we have the following representation
Estimate = 362 * 1.75 + 221 *2.35
Approximate
Estimate = 360 * 2 + 220 * 2
Hence, the expression is 360 * 2 + 220 * 2
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7
10
1
2/5
Cedric has
3
of the pie
of the pie
of the pie
of the nie
4
of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
C
PR
The fraction of the pie left that each friend will receive is; 3/8 of the pie
How to divide fractions?Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.
The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.
For example, 3/8 divided by 3/4 would be;
3/8 divided by 3/4 = 3/8 * 4/3
Now, we are told that cedric has 3/4 of a pie left.
Now, he wants to share equally among two of his friends, it means that;
Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8
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Complete question is;
Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
suppose that 15% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?
Probability that both the person own the dog is equal to 0.0225.
What is Probability ?The likelihood that an event will occur is measured by probability. It is difficult to provide a complete prediction for many events. Using it, we are only able to estimate the likelihood that an event will occur, or the chance that it will. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probabilities.
Let event A denotes that a person own dog,
P(A) = 15% =15/100 = 0.15
If we pick two people at Random then Probability that they both own dog
= P(A)*P(A)
= 0.15 * 0.15
= 0.0225
Required Probability = 0.0225
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please help me solve this asap
Answer: D. Vertical
Step-by-step explanation:
The zeros of a parabola are -5 and 2, and it passes through the point (1, -18). What inequality represents all the ordered pairs outside the parabola?
The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains al the ordered pairs outside the parabola.
What is the quadratic inequality of the parabola?
In this problem we must determine a quadratic inequality of the form:
a · x² + b · x + c < y
Where a, b, c are the real coefficients of the inequality.
First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:
25 · a - 5 · b + c = 0
4 · a + 2 · b + c = 0
a + b + c = - 18
(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)
Second, write the quadratic inequation:
(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
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A hockey goaltender has a save percentage of 0.920. This
means that the probability of any single shot taken on the
goaltender being a goal is 0.08. What would be the
expected number of goals scored on this goaltender in a
game where she faced 35 shots?
2.8 goals
2.0 goals
3.4 goals
1.5 goals
Answer:
2.8 goals
Step-by-step explanation:
35 * 0.08 = 0.35*8
0.35*8=2.8
The expected number of goals scored on the goaltender would be 2.8.
Explanation:The expected number of goals scored by the goaltender can be calculated using the formula:
Expected goals = Total shots * Probability of a goal
Therefore, for a goaltender with a save percentage of 0.920 (which means the probability of a goal is 0.08), and facing 35 shots:
Expected goals = 35 * 0.08Expected goals = 2.8The expected number of goals scored on this goaltender in a game where she faced 35 shots would be 2.8 goals.
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The video game club lost 8 members which was 28% of their group.
What was the original attendance of the video game club?
HELP!!!
The original attendance of the video game club was 28.57 members.
To determine the original attendance of the video game club, you can use the following formula:
Original attendance = (Number of members lost) / (Percent of group that left)
Plugging in the values from the problem, we get:
Original attendance = (8 members) / (28%)
To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:
Original attendance = (8 members) / (0.28)
Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:
Original attendance = 28.57 members
Therefore, the video gaming club had 28.57 members when it first started.
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Question 1 (1 point)
How many solutions does the system of equations have?
Answer: 0
Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.
Rewrite one eighteenthx3y + seven eighteenthsxy2 using a common factor.
one thirdxy(6x2 + 7y)
one thirdx2y(6x2 + 9y)
one eighteenthxy(x2 + 7y)
one eighteenthx3y2(y + 7)
Answer:
C
Step-by-step explanation:
1/18 x³y + 7/18 xy²
1/18 xy (x² + 7y)
Match the Vocab Word to the definition.
Remember, you are allowed to use your notes to help you!
Question 3 options:
If a = b, and c ≠ 0, then a/c = b/c
If a = b, then a + c = b + c
If a > b, and c > 0, then a/c > b/c
If a > b, and c < 0, then a/c < b/c
If a > b, then a - c > b – c
If a = b, then c ∙ a = c ∙ b
If a > b, and c > 0, then c ∙ a > c ∙ b
If a > b, and c < 0, then c ∙ a < c ∙ b
If a = b, then a - c = b - c
If a > b, then a + c > b + c
1.
Addition Property of Equality
2.
Subtraction Property of Equality
3.
Multiplication Property of Equality
4.
Division Property of Equality
5.
Addition Property of Order
6.
Subtraction Property of Order
7.
Multiplication Property of Order
8.
Division Property of Order
Match the Vocab Word to the definition
1. Addition Property of Equality
If a = b, then a + c = b + cIf a > b, then a + c > b + c2. Subtraction Property of Equality
If a = b, then a - c = b - cIf a > b, then a - c > b – c3. Multiplication Property of Equality
If a > b, and c > 0, then c ∙ a > c ∙ bIf a > b, and c < 0, then c ∙ a < c ∙ bIf a = b, then c ∙ a = c ∙ b4. Division Property of Equality
If a = b, and c ≠ 0, then a/c = b/cIf a > b, and c > 0, then a/c > b/cIf a > b, and c < 0, then a/c < b/cWhat is order property in math?Order property refers to situation of changing the order of the factors. swapping the positions of the addends still maintain the answer
For instance commutative property of addition
a + b = b + acommutative property of multiplication
a * b = b * aThe properties of equality refers to performing same operation in the opposite sides of an equation
Addition Property of Equality: here c is added to both sides of the equality such that a = b, then a + c = b + c
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Given OP bisects angle MON, PM is perpendicular to PM and PN is perpendicular to ON. Prove PN is congruent to PM
1. [tex]\overline{OP}[/tex] bisects [tex]\angle MON[/tex] (given)
2. [tex]\angle MOP \cong \angle PON[/tex] (definition of angle bisector)
3. [tex]\overline{PN} \perp \overline{ON}[/tex], [tex]\overline{PM} \perp \overline{OM}[/tex] (given)
4. [tex]\angle PNO[/tex] and [tex]\angle PMO[/tex] are right angles (definition of perpendicular lines)
5. [tex]\angle PNO \cong \angle PMO[/tex] (all right angles are congruent)
6. [tex]\overline{OP} \cong \overline{OP}[/tex] (reflexive property)
7. [tex]\triangle MOP \cong \triangle NOP[/tex] (AAS)
8. [tex]\overline{PN} \cong \overline{PM}[/tex] (CPCTC)
It is proved that PN is congruent to PM by CPCTC
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
We are Given OP bisects angle MON, PM is perpendicular to PM and PN is perpendicular to ON.
Therefore, Angle PNO and Angle PMO are right angles ( by definition of perpendicular lines)
All right angles are congruent;
Triangle PNO is congruent to Triangle PMO
OP = OP (by reflexive property)
Thus, MOP is congruent to NOP by AAS
PN = PM (CPCTC)
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What can use the distributive property to the algebraic expression 5(x - 7)
Usibg the distributive property to the algebraic expression 5(x - 7) will be 5x - 35.
What is distributive property?The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.
When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you want to multiply 5 by the product of 10 plus 3. When two terms are similar, we typically add the two numbers before multiplying by 5. However, the property states that you should first multiply each addend by 5.
Therefore, 5(x - 7) will be:
= 5(x) - 5(7)
= 5x - 35
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how much less is the value including 13% VAT in Rs.3200 than Rs.3820
The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."
Here, we have VAT.
A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.
Value on Rs. 3200 with 13% VAT
= 3200 + 30% of 3200
= 3200 + 960
= 4160 rupees
Now, the less value,
= 4160 - 3820
= 340 rupees.
Therefore, the less value is 340 rupees.
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what is the correct congruence statement for triangles shown
Answer:
It is NLJ
Step-by-step explanation:
Trust me lol
7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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What is the simplest form of (x^2+5x-6) / (x^2+9x+18)?
a) (x+2) / (x+6)
b) 1/3
c) (x-1) / (x+3)
d) -1/3
Answer:
a. [tex]\frac{x+2}{x+6}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]
at the city museum, child admission is $5.30 and adult admission is $9.80. on thursday, 143 tickets were sold for a total sales of $1149.40. how many adult tickets were sold that day?
The number of adult tickets which were sold that day as calculated from the given data is 29.
First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.
To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.
This is represented by the following equation,
$8.90A + $5.30C = $928
Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:
3 * C = A
Now we can answer our first problem by substituting 3 * C for A.
8.9 (3C) + 5.3C = 928
26.7C + 5.3C = 928
32C = 928
C = 29
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Which equation represents a hyperbola with a center at (0,0) a vertex at (-48,0) and a focus at (50,0)
The equation of hyperbola will be;
⇒ x²/48² - y²/14² = 1
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
In hyperbola,
The value of center = (0, 0)
The value of vertex = (- 48, 0)
The value of focus = (50, 0)
Now,
We know that;
The equation of hyperbola is,
⇒ (x - h)²/a² - (x - k)²/b² = 1
Where, (h, k) is center, (h ± a, k) is the vertex.
Here, The value of center = (0, 0)
The value of vertex = (- 48, 0)
The value of focus = (50, 0)
So, h = 0, k = 0
a = 48, c = 50
We get;
⇒ (x - 0)² / 48² - (y - 0)² / b² = 1
⇒ x² / 48² - y² / b² = 1
Since, c = √a² + b²
⇒ b = √c² - a²
⇒ b = √50² - (-48)²
⇒ b = √196
⇒ b = 14
Hence, We get;
⇒ x² / 48² - y² / b² = 1
⇒ x² / 48² - y² / 14² = 1
Thus, The equation of hyperbola is;
⇒ x²/48² - y²/14² = 1
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The area of the caribbean sea is 2.7182 × 106 km2. the area of the south atlantic ocean is 4.027 × 107 km2. find the total area. write the final answer in scientific notation with the correct number of significant digits. 4.29882 × 108 km2 4.299 × 107 km2 3.75518 × 1013 km2 3.755 × 1013 km2
The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²
Calculating total areaFrom the question, we are to determine the total area of the water bodies.
From the given information
"The area of the Caribbean sea is 2.7182 × 10⁶ km²"
and
"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"
To determine the total area, we will add up the two areas
Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²
Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²
Total area = 4.29882 × 10⁷ km²
Total area ≈ 4.299 × 10⁷ km²
Hence, the total area is 4.299 × 10⁷ km²
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Answer:
Hence, the total area is 4.299 × 10⁷ km²
Step-by-step explanation:
A car traveled at an average speed of 60 mph for two hours. how far did it travel? responses 30 miles 30 miles 60 miles 60 miles 120 miles 120 miles 150 miles
Answer: 120 miles
Step-by-step explanation:
If a car goes 60 miles per hour then in two hours (60×2) it will go 120
fillings how much do prices vary for filling a cavity? to find out, an insurance company randomly selects 10 dental practices in california and asks for the cash (non-insurance) price for this procedure at each practice. the interquartile range is $74.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.
2. The insurance company then computes the interquartile range of the prices for each practice.
3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
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In a recent poll, 45% of adults took 2 weeks' vacation in 2017, and 23% of adults took 2 weeks' vacation and went out of the country. What is the probability that an adult went out of the country given they took 2 weeks' vacation?
The probability that an adult went out of the country given they took 2 weeks' vacation is 51%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that in a recent poll, 45% of adults took 2 weeks' vacation in 2017, and 23% of adults took 2 weeks' vacation and went out of the country.
The probability will be calculated as,
Probability = (23 / 45) x 100
Probability = 0.51 x 100
Probability = 51%
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Solve for y in this diagram. Justify your answer.
The value of y in the isosceles triangle is AC = 6 cm
What Is an Isosceles Triangle?
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ABC
Now , the angle ∠ABC = 25°
The angle ∠ACB = 25°
So , the 2 angles of a triangle is 25° so , the third angle is 130°
So , the triangle is an isosceles triangle
And , the two sides of the triangle is AB = AC
The measure of side AB = 6 cm
The measure of side AC = measure of side AB
Therefore , the measure of side AC = 6cm
Therefore , the value of AC is 6 cm
Hence , the measure of side AC of triangle is 6 cm
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Which parent function is represented by the graph?
O A. An exponential parent function
• B. The quadratic parent function
• C. The absolute value parent function
O D. The linear parent function
Parent function is represented by the graph is
B. The quadratic parent function
What is Parent function?
A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.
A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.
The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.
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