The linear equation that passes through the point (2,-9) and has a slope of -5 in slope-intercept form is y = -5x = 1
How to represent linear equation?Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.
Hence, the linear equation in slope intercept form is as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (2,-9) and has a slope of -5 .
Hence,
y = -5x + b
let's find the y-intercept using (2, -9)
-9 = -5(2) + b
-9 = -10 + b
b = -9 + 10
b = 1
Therefore, the linear equation is y = -5x + 1
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Simon bought a $48 table on sale at 30% off.
Select from the drop-down menu to correctly complete the sentence
0.03(50)
0.3(50)
3(50)
30(50).
Simon bought a $48 table on sale. The price of the table can be estimated by $50.
The sale propose 30% off, then an estimate for the discount can be calculated using proportion:
$50 -- 100%,
$x -- 30%
that is mathematically
Find x:
Answer: correct choice is B
5. Solve the inequality. Graph the solution.
T-9 <-6
Answer:
b
Step-by-step explanation:
because you solve it and you get B
Josh loves to visit his aunt's house. When there, his two favorite activities are walking the dog and playing darts. Let A represent the event that he walks his dog at his aunt's house and B represent the event that he plays darts at his aunt's house. If A and B are independent events with P(A)=0.9 and P(B)=0.4, find P(A AND B).
The probability of P(A AND B) when Josh visit his aunt's house is 0.36.
What is probability?Probability is the likelihood that an event will occur or take place.
Let A = the event that he walks his dog at his aunt's house
Let B = the event that he plays darts at his aunt's house.
When A and B are independent events with P(A)=0.9 and P(B)=0.4, the probability of P(A AND B) will be:
= P(A) × P(B)
= 0.9 × 0.4
= 0.36
The probability is 0.36.
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Please i need help urgently thanks
Answer:
Step-by-step explanation:
rate of change
[tex]=\frac{f(b)-f(a)}{b-a} \\=\frac{f(9)-f(1)}{9-1} \\=\frac{28-20}{8} \\=\frac{8}{8} \\=1[/tex]
-1/2u+3/5=1/6 What is u?
_____________________
[tex]\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}[/tex]
[tex]u=\frac{13}{15}[/tex][tex]\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}[/tex]
DefinitionsMultiplication - Multiplication, otherwise known as the inverse of division repeats a certain number's value into what it has been multiplied by. Ex. [tex]4\cdot4=16[/tex]
Fraction - A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.
Algebra - Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all mathematics
Reciprocal - In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by [tex]\frac{1}x[/tex] or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction [tex]\frac{a}b[/tex] is [tex]\frac{b}a[/tex]. For the multiplicative inverse of a real number, divide 1 by the number.
_____________________
Now we can solve this equationStep one - Subtract: [tex]-\frac{1}{2} u=\frac{1}{6}-\frac{3}{5}[/tex]Step two - Simplify: [tex]-\frac{1}{2} u=-\frac{13}{30}[/tex]Step three - Multiply by the reciprocal of [tex]-\frac{1}2[/tex]: [tex]-\frac{1}{2}u\cdot -\frac{2}{1}=-\frac{13}{30}\cdot -\frac{2}{1}[/tex]Step four- Simplify: [tex]u=\frac{13}{15}[/tex]Your answer is [tex]u=\frac{13}{15}[/tex]find the missing value ratio inches :2 and years: 3,1,8
Answer: The missing values in the ratio table will be 0.666 and 5.33 inches.
Step-by-step explanation:
As the ratio of the terms is equal. The value of x and y is ,
2/3 = x/1
x=2/3
x=0.66 inches
In order to obtain y,
2/3 = y/8
y=2×8/3
y=16/3
y=5.33 inches.
Determine the slope-intercept form of the equation of the line parallel to y = -4/3x + 11 that passes through the point (–6, 2). y = x +
The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
According to the question,
We have the following information:
The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).
Now, we know that the following formula is used to find the equation of the line:
y-y' = m(x-x')
In this case, m is the slope of the line.
m = -4/3
We have the following values:
x' = -6 and y' = 2
Now, we have the following expression:
(y-2) = -4/3(x+6)
y-2 = -4x/3-8
Adding 2 to both sides of the equation:
y = -4x/3-8+2
y = -4x/3-6
Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
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Answer the question in the picture.
(MARKING BRAINLIEST) Maggie and Katie go out to dinner there a bill comes to $64.50 they are required to pay 8.5% sales tax what is the total amount Maggie and Katie have to pay ?
Answer:
$69.98
Step-by-step explanation:
8.5% of 64.50 is around 5.48 or to be exact, 5.4825 which there are no more dollar denominations beyond the hundredth place so it would be 5.48. 64.50+5.48 is $69.98.
Answer:
$69.98
Step-by-step explanation:
It is percent increase.
So, 100% + 8.5% = 108.5% which is 1.085.
64.50 × 1.085 = 69.9825
we need to round to 2 decimal places
$69.98
pls help with this . give only what it ask for the answers.
Answer:
(10, -1)
Step-by-step explanation:
x + 2x = 3x
-y + y = 0
11 + 19 = 30
3x = 30
3/3 x = 30/3
x = 10
10 - y = 11
y = -11 + 10
y = -1
Given that logb(7)≈1.946, logb(9)≈2.197, and logb(16)≈2.773, find the logarithm of logb(1/63)
b is base b
The logarithmic expression given as logₙ(1/63) has its value to be -4.143
How to determine the logarithmic expression?From the question, the given parameters are
logₙ(7) = 1.946
logₙ(9) = 2.197
logₙ(16) = 2.773
The logarithmic expression to calculate is given as
logₙ(1/63)
Express 1/63 as 1/7 * 1/9
So, we have the following representation
logₙ(1/63) = logₙ(1/7 * 1/9)
Apply the product of logarithm
This gives
logₙ(1/63) = logₙ(1/7) + logₙ(1/9)
Apply the exponent of logarithm
This gives
logₙ(1/63) = -logₙ(7) - logₙ(9)
Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)
logₙ(1/63) = -1.946 - 2.197
Evaluate
logₙ(1/63) = -4.143
Hence, the value of the logarithmic expression is -4.143
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a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
a) The test statistic is: t = -1.11.
b) The p-value is: 0.1342.
c) The conclusion is that the null hypothesis is not rejected.
d) The final conclusion is that there is not sufficient evidence to conclude that the population mean is of 6.
What is the test statistic?The standard deviation for the population is unknown, only the sample standard deviation is known, hence the t-distribution is obtain the test statistic.
The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the variables of the equation are given as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.For this problem, the values of these parameters are as follows:
[tex]\overline{x} = 5.83, \mu = 6, s = 2.11, n = 189[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{5.83 - 6}{\frac{2.11}{\sqrt{189}}}[/tex]
t = -1.11.
P-value and conclusionThe p-value is obtained using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less a value, with 189 - 1 = 188 df and t = -1.11, hence it is of 0.1342.
Since the p-value is greater than the significance level of 0.10, it is found that:
The null hypothesis is not rejected.There is not sufficient evidence to conclude that the population mean rating is less than 6.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
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Write three quadratic equations that are NOT equivalent, each forming a graph with vertex
(−2,3).
Please explain it
When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).
The vertex of a quadratic equation:
a[tex]x^{2}[/tex]+bx + c = y
is located at :
x = -b/2a.
In this case, x = -2
Then,
-b/2a = -2
And we also have that:
a[tex](-2)^2[/tex] -2b + c = 3
Then we have two equations:
-b/2a = -2
a[tex](-2)^2[/tex] -2b + c = 3
We have only equations and 3 variables, So we can just give the variable c different values and we will find different quadratic equations that are not equivalent.
Let's begin with c = 0 ,Our equations are:
-b/2a = -2
a[tex](-2)^2[/tex] -2b + 0 = 3
In the first equation we can isolate b and get :
b = 4a
Now we can replace this in the other equation and solve this for a.
4a + 4a x -2 = 3
-4a = 3
a = -3/4
then:
b = 4a = 4 x -3/4 = -3
The first quadratic equation is:
(-3/4)[tex]x^{2}[/tex] - 3x = y
Now, To find the second let's use a different value of c.
c = 1
b = 4a
a[tex](-2)^2[/tex] -2b + 1 = 3
Let's solve in the same way as before:
4a + 4a x -2 + 1= 3
-4a = 2
a = 2/-4 = 1/-2
b = 4 x -1/2 = -2
Then our equation is :
(-1/2)[tex]x^{2}[/tex] -2x + 1 = y
For the last equation, let's use c = 2
then our equation are:
b = 4a
a(-2)^2 - 2b +2 = 3
Same as before, replace the first equation in the second
4a + 4a x-2 +2 = 3
-4a +2 = 3
-4a = 1
a = -1/4
Then:
b = 4 x (-1/4) = -1
Our third equation is :
(-1/4)x^2 - x + 2 = y
Now, Below you can see all of them graphed.
When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).
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Question content area top
Part 1
Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Perpendicular to the line y=
1
2x−2; containing the point (−3,6)
The equation of the line in slope-intercept form is y = -x/12 + 23/4
How to find the equation of the line?Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of a straight line is:
y = mx + c,
where m is the slope and c is the y-intercept
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
y = 12x−2 and m₁ x m₂ = 12
m₁ x m₂ = -1
12 x m₂ = -1
m₂= -1/12
Line 2(unknown) with the point (−3,6):
y = mx + c
6 = -1/12 (-3) + c
6 = 1/4 + c
c = 6 -1/4 = 23/4
y = -x/12 + 23/4
Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4
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A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.” If a simple random sample of 50 adult Americans is collected, what is the probability that more than one-fourth of them will have low levels of literacy as described above?
The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.”
A simple random sample of 50 adult Americans is collected.
n(p) = 50(0.22)
n(1 - p) = 50(1 - 0.22)
The CLT would hold here.
n = 50
p = 0.22
p cap = 0.25
The test statistic, z = (p cap - p) / (√p (1 - p) / n)
z = (0.25 - 0.22)/(√0.22(1-0.22)/50)
z = 0.51
The p-value is 0.3043.
Hence, The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.
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Which table represents a function?
Answer:
C (the one which starts with x = -2 and y = -1)
Step-by-step explanation:
because for every x value there is only an y value
PLEASE HELP ME !!!
x² + 12x -
2
8 can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Answer:
a = 6 , b = - 44
Step-by-step explanation:
x² + 12x - 8
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² from x² + 12x
x² + 2(6)x + 36 - 36 - 8
= (x + 6)² - 44 ← in the form (x + a)² + b
with a = 6 and b = - 44
If x = -4 and y = 3, what is the value of 1/2x + 3xy^2
If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
What is a value function?
The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.
What is a variable?
A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.
Here, we have
x = -4 and y = 3
then by putting the value of a function in a given equation, we get
1/2*(-4) + 3*(-4)*(3)²
= -110
Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
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Helpi really need this
Answer:
The height of the flagpole is about 25.6 feet.
Step-by-step explanation:
The figure is omitted--please sketch it.
Put your calculator in degree mode.
Let h be the height of the flagpole.
[tex] \tan(52) = \frac{h}{20} [/tex]
[tex]h = 20 \tan(52) = 25.6[/tex]
Simplify completely. 3x+18 divided 18
solution
3x+18/18
ans4
Write and solve a proportion for each word problem.
(9)There are 9 strawberries in a quart package. How many
quart packages do you need if you want 62 strawberries?
We will need 7 quart package if we want 62 strawberries
What is division?
Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.
We are given that there are 9 strawberries in a quart package
Also we want 62 strawberries
Then how many quart will be required
Now we perform division to find the number of quart
62/9 = we get a value of 8.88
Which is very close to nine
Hence we will need 9 quart packages if we want 62 strawberries
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Is the function that cuts through the points (2, 3) and (-1, 6) increasing or decreasing? a. increasing c. neither b. decreasing d. cannot be determined Please select the best answer from the choices provided A B C D Mark this and return
Solve for x.
please help! giving 20 points
Can you help me with this problems, thank you.
The probability that student will pass the test is 2/7.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.So, the probability that the student will pass the test:
The total number of questions are 50 and 25 questions need to be correct to pass the test.Out of 25, 15 are correct.Out of the remaining 35 questions, 10 questions need to be right to pass the best.Probability Formula: P(E) = Favourable events/Total events
Now, calculate as follows:
P(E) = Favourable events/Total eventsP(E) =10/35P(E) = 2/7Therefore, the probability that student will pass the test is 2/7.
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The radius of the circle below is 27 mm.
Calculate the area of the circle.
Give your answer in mm² to 1 d.p.
27 m
84.78 mm² is area of circle .
What is a circle ?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center.Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry.radius of the circle = 27 mm
area of the circle = πr²
= 3.14 * 27
= 84.78 mm²
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If 3/5 of a number is 150, what is the number
let the number be = x
step by step explanation:[tex] = > \frac{3x}{5} = 150[/tex]
Cross multiply:[tex] = > 3x = 150 \times 5[/tex]
[tex] = > 3x = 750[/tex]
Divide both side by 3[tex] = > \frac{3x}{3} = \frac{750}{3} [/tex]
[tex] = > x = 250[/tex]
The number can be found by multiplying 150 by 5 and then dividing the result by 3. Therefore, the number is 250 by solving equations.
To find the number, we can set up the equation: (3/5) * x = 150. To isolate x, we multiply both sides of the equation by 5/3, resulting in x = 250. This means that the number is 250.
Start with the equation: (3/5) * x = 150.
To isolate x, multiply both sides of the equation by the reciprocal of (3/5), which is 5/3. This yields (5/3) * (3/5) * x = (5/3) * 150.
Simplify the left side of the equation: x = (5/3) * 150.
Multiply 5 by 150 and divide the result by 3: x = (750/3).
Simplify the fraction by dividing the numerator (750) by the denominator (3): x = 250.
Therefore, the number is 250.
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Dave's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 yards of tape. Dave's group decides to roll up each of their newspapers. Then, they tape each roll with 4 inches of tape. How many inches of tape do they have left?
32 inches more of tape students need.
Given that,
Students in Dave's science class are trying to build the tallest structure. Ten newspapers and two yards of tape are given to each group of kids. The decision is made by Dave's group to roll up each newspaper. Then, they use 4 inches of tape to seal each roll.
We have to find how many more inches of tape are there.
We know that,
1 yard is 36 inches.
So,
2 yards is 2 times 36 is 72 inches.
The inches of the tape they need is 10 times 4 is 40.
So,
72-40 is 32 inches
Therefore, 32 inches more of tape students need.
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Raina, Trey, and Deandre have a total of $145 in their wallets. Raina has $10 more than Trey. Deandre has 3 times what Raina has. How much do they have in their wallets?
Trey, Raina, and Deandre have $21,$31, and $93 in their wallets respectively.
From the question the sum of the money in their wallets is:
Raina + Trey +Deandre=$145
R + T + D =$145................(i)
Raina has $10 more than Trey= ($10 + T)
Deandre has 3 times more Raina =3($10 + T)
substituting the values of Raina and Deandre in Eqn (i) we have
R + T + D =$145
($10 + T) + T +{3$(10 + T)}=$145
$10 +T +T+ $30 + 3T =$145
5T +$40 = $145
5T = $145 - $40
5T = $105
T = $105/5
T = $21
i.e Trey = $21
Raina has $10 more than Trey= ($10 + T)
i.e = ($10 + $21)
Raina =$31
Deandre has 3 times more Raina =3($10 + T)
=3($10 + $21)
=$30 +$63
Deandre =$93
Therefore the total sum of money in thier wallet is:
Raina + Trey +Deandre=$145
$31 + $21 + $93= $145
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PLEASE HELP ASAP!!! I WILL MARK YOU YOU BRAINLIEST
Which equations are true equations?
Select all correct answers.
39-3-6 6-10 +4
56 +8+3² - 2.2³
=
24
04-50-6²-8
82 5² 4² - 7
=
-
-
Answer:
C and A
Step-by-step explanation:
i need help with this pls
Option C: The relationship between the statement cannot be determined.
What is Conditional statement?
Two independent statements can be related to each other in a logic structure called a conditional statement.
The first statement is presented with “if,” and is referred to as the hypothesis.
The second statement is linked with “then”, and is known as the conclusion.
The notation associated with conditional statements typically uses the variable p for the hypothesis statement, and q for the conclusion.
p → q
Explanation for the answer:
The converse statement is notated as q→p (if q, then p). The original statements switch positions in the original “if-then” statement.The inverse statement assumes the opposite of each of the original statements and is notated ∼p→∼q (if not p, then not q).The contrapositive statement is a combination of the previous two. The positions of p and q of the original statement are switched, and then the opposite of each is considered: ∼q→∼p (if not q, then not p).
So, from the above we can clearly see that the both the statement 1 and statement are not start with "if" and "then".
Therefore, their relationship cannot be determined.
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