Answer:
[tex]\large\boxed{y=-\frac{3}{2}x+\frac{3}{2}}[/tex]
Step-by-step explanation:
Use the two-points slope equation: [tex]\boxed{m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
Given the two coordinate points of [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex], implement these values into the equation and solve for m.
[tex]m=\frac{(3)-(6)}{(-1)-(-3)}\\\\m=\frac{(-3)}{(2)}\\\\m=-\frac{3}{2}[/tex]
The slope is then placed in the equation - y = -3/2x + b.
Then, insert a value for y and x from the same coordinate point to solve for b.
[tex]6=-\frac{3}{2}(-3)+b\\\\6=\frac{9}{2}+b\\\\\frac{3}{2}=b[/tex]
Then, plug it all in to get [tex]\large\boxed{y=-\frac{3}{2}x+\frac{3}{2}}[/tex].
Answer:
y=-3/2x
Step-by-step explanation:
First, find the slope with y2-y1/x2-x1=m
3-6 m=-3/2
--------- =
-1-+-3
Now plug it in to point slope form
Point slope form is y-y1=m(x-x1)
y-3=-3/2(x--1) Distribute -3/2 to x and 1
y-3=-3/2x-3 Add three on both sides to get y alone
y=-3/2x Three's cancel out. This is the final equation.
Select the correct answer.
What is the product of (x - 3) and (x + 7)?
[tex] {x}^{2} + 10 - 21[/tex]
Answer:
[tex] \boxed{ \boxed{ \bold{ {x}^{2} + 4x - 21}}}[/tex]Step-by-step explanation:
[tex] \sf{(x - 3)(x + 7)}[/tex]
Use the distributive property to multiply each term of the first binomial by each term of the second binomial.
⇒[tex] \sf{x(x + 7) - 3(x + 7)}[/tex]
⇒[tex] \sf{ {x}^{2} + 7x - 3x - 21}[/tex]
Collect like terms
⇒[tex] \sf{ {x}^{2} + 4x - 21}[/tex]
Hope I helped!
Best regards!!
Answer:
[tex] \boxed{\boxed{\boxed{\red{{x}^{2} + 4x - 21}}}}[/tex]
Step-by-step explanation:
[tex](x - 3)(x + 7) \\ x(x + 7) - 3(x + 7) \\ {x}^{2} + 7x - 3x - 21 \\ {x}^{2} + 4x - 21[/tex]
Why are integers the same as rational numbers
Answer:
The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction a/b, where a and b are integers. If a number is a whole number, for instance, it must also be an integer and a rational.
Step-by-step explanation:
While traveling in England, Sonia noticed that the price of gas was 1.4 pints per liter. She wondered how that compares to the price of gas in Atlanta, where she lives. On that day, the exchange rate was £1= $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1L=0.26 gal.
Answer:
$8.40
Step-by-step explanation:
Price in England = 1.4 pounds per Litre
Current exchange rate : 1 pound = 1.65 dollars
1 Litre = 0.26 gallons
If 1 Litre = 0.26 gallons
1 gallon = (1 / 0.26) litres = 3.8461538 litres
Therefore, cost per gallon in England = (1.4 × 3.8461538)
= 5.3846153 pounds
Then ;
If 1 pound = 1.56 dollars
Then cost per gallon in dollars equals
5.3846153 * 1.56 = 8.399999868 dollars
$8.40
Find the perimeter of the rectangle
10x - 3
2x + 6
Answer:
[tex]24x+6[/tex]
Step-by-step explanation:
We know that the perimeter of a rectangle's formula is [tex]2l + 2w = p[/tex], where l is the length and w is the width - p is the perimeter. We know the length and width, so we can substitute into the equation.
[tex](2\cdot(10x-3)) + (2\cdot(2x+6))\\\\(20x-6) + (4x+12)[/tex]
We can now combine like terms to get [tex]24x + 6[/tex].
Hope this helped!
Translate 5 times the sum of 7 and n
Answer:
5( 7+n)
Step-by-step explanation:
First find the sum
(7+n)
Then multiply by 5
5( 7+n)
Answer:
[tex]\Huge \boxed{5(n+7)}[/tex]
Step-by-step explanation:
The sum of 7 and n is also adding 7 and n.
[tex]7+n[/tex]
The sum is the result from adding. That result is multiplied by 5.
[tex]5 \times (7+n)[/tex]
[tex]5(n+7)[/tex]
HELP PLS!! 50 POINTS
Answer:
5 ^ (1/12)
Step-by-step explanation:
5 ^ 1/3
-----------------
5 ^ 1/4
When we divide exponents with the same base, we subtract the exponents
5 ^ (1/3 -1/4)
Getting a common denominator
5 ^ ( 4/12 - 3/12)
5 ^ (1/12)
Answer:
[tex]\Huge \boxed{5^{\frac{1}{12}}}[/tex]
[tex]\rule[225]{225}{3}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sf \frac{5^{\frac{1}{3}} }{5^{\frac{1}{4}} }[/tex]
When dividing same bases, we subtract the exponents.
[tex]\displaystyle \sf 5^{\frac{1}{3}- \frac{1}{4} }[/tex]
Making exponents have the same denominator.
[tex]\displaystyle \sf 5^{\frac{4}{12}- \frac{3}{12} }[/tex]
Subtracting exponents.
[tex]\displaystyle \sf 5^{\frac{1}{12}}[/tex]
[tex]\rule[225]{225}{3}[/tex]
8a + 16[tex]8a + 16[/tex]
Answer:
8(a+2)
Step-by-step explanation:
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Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .?
Answer:
-2
Step-by-step explanation:
-12 -14
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The function for the cost of materials to make a hat is f(x) = 1/2x + 1, where x is the number of hats. The function for the selling price of those hats is g(fx)), where g(x) = x + 2. Find the selling price of 10
hats.
Answer:
8 dollars
Step-by-step explanation:
f(10)=6
g(6)=8
8 dollars
Given IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15, the proportion of people with IQs above 130 is:
Answer: 0.0228 .
Step-by-step explanation:
Given, IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15
Let X denotes the IQ score.
Then, the proportion of people with IQs above 130 is
[tex]P(X>130)=P(\dfrac{X-mean}{ standard\ deviation}>\dfrac{130-100}{15})\\\\= P(Z>2)\ \ \ \[Z=\dfrac{X-mean}{ standard\ deviation}][/tex]
[tex]=1-P(Z<2)\ \ \ [P(Z>z)=1-P(Z<z)]\\\\=1-0.9772\ [\text{By z table}]\\\\=0.0228[/tex]
Hence, the proportion of people with IQs above 130 is 0.0228 .
suppose y varies jointly as x and z. Find y when x=5 and z=6, if y=144 when x=6 and z=10
Answer:
y=72
Step-by-step explanation:
y varies jointly as x and z
y=k*x*z
Where,
k= constant of proportionality
y=144, x=6, z=10
y=k*x*z
144=k*6*10
144=60k
Divide both sides by 60
144/60=k
2 24/60=k
2 6/15=k
2 2/5=k
k=12/5
Find y when x=5 and z=6
y=k*x*z
y=12/5*5*6
=360/5
=72
y=72
In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables?
Answer: The correlation between variables must be significant
Step-by-step explanation: In order to make reliable predictions using the equation of a regression model, the correlation Coefficient between the dependent and independent variables must be significant (that is a correlation Coefficient value close to either 1 or - 1). This is because the range of value of the correlation Coefficient is between - 1 to +1 and the closer the correlation Coefficient value is to either of these numbers, depicts the strength of the relationship which exists between them hence, enabling us to make good and accurate predictions which are close to the actual value.
Regression Analysis is a statistical and reliable process for making predictions using the regression model.
The correct option is:
Option B. The correlation between variables must be significant
The regression line can be explained as:
1. The correlation coefficient between the dependent and independent variables must be significant.
2. The correlation coefficient value should be near 1 or -1.
3. Thus, the values closer to - 1 and +1 will depict the strength of the relationship between the coefficient values.
Thus, regression lines help to predict accurate and reliable results that are close to the actual value.
To know more about regression lines, refer to the following link:
https://brainly.com/question/4341286
Q5. A farm raises cows and chickens. The farmer has a total of 42 animals. One day he counts the legs of all of his animals and realizes he has a total of 114.
a) How many cows does the farmer have?
b) How many chickens?
c) What is the importance of farmer?
Answer:
let cow=x and chickens =y
cows have 4 legs, 4x. chickens have 2 legs, 2y
Answer:
a= 15 cows b= 27 chickens c= none, he is not an animal.
Step-by-step explanation:
cows have four legs
chickens have two
15 cows = 60 legs
27 chickens = 54 legs
60+54 = 114
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barons "A salad bar has 7 ingredients, excluding the dressing. How many different salads are possible where two salads are different if they don't include identical ingredients?"
Answer: 128
Step-by-step explanation:
Given : Total ingredients =7
When we select any one of ingredient for salad, then total choices for each ingredient = 2 (Yes or No)
So for all 7 ingredients there will be [tex]2\times2\times2\times2\times2\times2\times2=2^7=128[/tex] choices [By fundamental principle of counting]
Hence, there are 128 different salads are possible where two salads are different if they don't include identical ingredients
25x^2- 100
What’s the factor
please help me on this
Answer:
AX = 14
Step-by-step explanation:
The medians of a triangle intersect at its centroid.
The position of the centroid X from the vertex A is
AX = [tex]\frac{2}{3}[/tex] AL = [tex]\frac{2}{3}[/tex] × 21 = 14
Richard purchased some books for $9.25 each. He paid a total of $46.25. If b is the number of books, which equation can be used to determine the total amount of books Richard bought? b + 9.25 = 46.25 46.25b = 9.25 9.25b = 46.25 46.25 - b = 9.25
Answer:
9.25b=46.25
Step-by-step explanation:
9.25b=46.25/:9.25
b=5
Richard purchased 5 books for $9.25 each
9. If DF = 61 and EF = 18, find DE.
Answer:
43 if yousubtract it
STEP-BY-STEP EXPLANATION
What slope is parallel to m=3/4
Answer:
[tex]\large \boxed{{m= \frac{3}{4} }}[/tex]
Step-by-step explanation:
Parralel lines have the same slope.
The slope will be [tex]\frac{3}{4}[/tex]
Zara filled up her car with 15 gallons of gas. If Zara paid $33.00, what was the price per gallon of gas?
Answer:
$2.20 per gallon.
Step-by-step explanation:
That is 33/15 = $2.20 per gallon.
Answer:
Step-by-step explanation:
Price per gallon = Total price of 15 gallons ÷ 15 gallons
= 33 ÷ 15
= $ 2.20
Lana had 8 4/6 cups of flour. If she used 6 1/6 cups of flour, how much flour
did she have left?
Answer:
2 3/6 or 2 1/2
Step-by-step explanation:
8 4/6 - 6 1/6 = 2 3/6
A 30 ft cable extends from the floor of the lookout of a fire tower. The table is anchored from the ground 18 ft away from the base of the tower. What is the Hight of the floor of the look out tower.
=================================================
Explanation:
Assume the ground is completely flat and level. We have a right triangle with hypotenuse 30, and the horizontal base leg is 18. The vertical leg is unknown, so we'll call it x.
Use the pythagorean theorem to solve for x
a^2+b^2 = c^2
x^2+18^2 = 30^2
x^2 + 324 = 900
x^2 = 900 - 324
x^2 = 576
x = sqrt(576)
x = 24
The height of the tower's floor is 24 feet.
witch is the warmer temperature -9°F or -7°F
Answer:
-7°F
Step-by-step explanation:
At first, you might think that the answer is -9 because 9 > 7, right? Actually, the "rules" for numbers are switched when you are dealing with negative numbers. Therefore, -7 > -9 so -7°F is the correct answer.
EVALUATE the expression
5x
—
2
for x= -3
Solve for the value of x.
5^x+1= 5^2x-3
Answer:
4
Step-by-step explanation:
5ˣ⁺¹ = 5²ˣ⁻³
x+1 = 2x -3
x = 4
Evaluate − 3 w − 5 p for w = − 4 and p = − 3
Answer:
27
Step-by-step explanation:
Given
- 3w - 5p ← substitute w = - 4 and p = - 3 into the expression
= - 3(- 4) - 5(- 3 )
= 12 + 15
= 27
hey can u pls answer this question i am really stuck I will award brainliest for the first correct answer
Answer for the first box = 6000
Answer for the second box = 1.004
Answer for the third box = 720
So the full equation is [tex]C(t) = 6000(1.004)^{12t} + 720t[/tex]
=======================================================
Explanation:
The compound interest formula is
A = P( 1+r/n )^(n*t)
where
P = amount deposited (principal)r = interest rate in decimal formn = number of times we compound per year (compounding frequency)t = number of yearsIn this case,
P = 6000r = 4.2% = 4.2/100 = 0.042n = 12 since there are 12 months in a year (it explains the 12 in the exponent in the answer)t = unknown, we leave this as isSo we go from this
A = P( 1+r/n )^(n*t)
to this
A = 6000( 1+0.042/12 )^(12t)
A = 6000(1.0035)^(12t)
A = 6000(1.004)^(12t)
The 1.0035 rounded to 1.004 when rounding to three decimal places, as the instructions mention.
So far we only considered the amount placed into the bank. But there's also the amount placed in the safe at home. We have $60 placed in here per month. This is 60*12 = 720 dollars per year. If t years go by, then a total of 720t dollars is put in the safe.
----------
So in summary we found
[tex]b(t) = 6000(1.004)^{12t}[/tex] = amount in savings account after t years go by
[tex]h(t) = 720t[/tex] = amount in safe after t years
leading to
[tex]C(t) = b(t) + h(t) = 6000(1.004)^{12t} + 720t[/tex]
Write the equation of the line in standard form
64. contains (-8, 4)
and the midpoint of the
segment connecting
(-10, 5) and (-5, 0). Show your work.
Answer:
[tex]\bold{3x+y+20=0}[/tex]
Step-by-step explanation:
Mid point of (-10, 5) and (-5, 0).
Other point (-8, 4).
To find:
Equation of line in standard form that connect the mid point and other point.
Solution:
Mid point formula is given as:
[tex]x = \dfrac{x_1+x_2}{2}\\y = \dfrac{y_1+y_2}{2}[/tex]
[tex]x = \dfrac{-10+-5}{2} = -7.5\\y = \dfrac{5+0}{2} = 2.5[/tex]
Now, the two points are: (-7.5, 2.5) and (-8, 4)
Slope intercept form of line is given as:
[tex]y = mx+c[/tex]
[tex]m=\dfrac{4-2.5}{-8-(-7.5)} = -3[/tex]
So, the equation of line is:
[tex]\Rightarrow y =-3x+c[/tex]
Putting (-8, 4) to find c:
[tex]4=-3\times -8+c\\\Rightarrow c = -20[/tex]
Equation of line:
[tex]\Rightarrow y =-3x-20[/tex]
In standard form:
[tex]\bold{3x+y+20=0}[/tex]
Express 25 minutes as a fraction of 2 hours in its simplest form
Answer:
5/24
Step-by-step explanation:
1 hour = 60 minutes
2 hours = 60*2 = 120 minutes
then:
25 minutes / 120 minutes
25/5= 5
120/5 = 24
the simpliest form is:
5/24
The simpliest form of 25 minutes as a fraction of 2 hours is 5/24
What is a fraction?A fraction represents a part of a number or any number of equal parts.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
We need to express 25 minutes as a fraction of 2 hours in its simplest form.
Since we know that 1 hour = 60 minutes
2 hours = 60 x 2 = 120 minutes
then:
25 minutes / 120 minutes
25/5= 5
Thus 120/5 = 24
Hence, The simpliest form of 25 minutes as a fraction of 2 hours is 5/24
Learn more about fraction;
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What is the slope form equation?
Answer:
y= mx +c
Step-by-step explanation:
The point- slope form of an equation is
y= mx +c, where m is the gradient and c is the y-intercept.
You can find the value of m by using the gradient formula.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Then substitute the value of m found into the equation. Next substitute a pair of coordinates the line passes through to find the value of c. Substitute the value of c and you will obtain the point-slope form equation of the line.
Here's an example.
Point-slope form of an equation passing through (1, 2) and (5, 6).
① Finding gradient, m.
[tex]m = \frac{6 - 2}{5 - 1} \\ m = \frac{4}{4} \\ m = 1[/tex]
② Substitute value of m into equation.
y= 1x +c
y= x +c
③ Substitute a pair of coordinates.
when x=1, y=2,
2= 1 +c
c= 2 -1
c= 1
Thus the equation of the line is y= x +1.
You may already know that "y+MX+b" form called the slope-intercept form of the equation of a line. It is the same equation in a different form. The 'b' value called the y intercept is where the line crosses the y- axis
Step-by-step explanation: