The number of solutions in the system is 1
How to determine the count of the solutions?From the question, the system of equations is given as
A linear equationA quadratic equationAlso, we understand that the linear equation is a vertical straight line.
So, we have the system to be
A vertical-line linear equationA quadratic equationA vertical line can only intersect with a quadratic line at one point
Hence, there is only one solution in the system
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Given the perimeter of 225 ft. Solve for x and then find the indicated side lengths.
Answer:
X=14
Side GF: 41 ft
Side FE: 58 ft
Side DE: 98 ft
Side DG: 28 ft
Step-by-step explanation:
(13+2x)+(4x+2)+(7x)+(X+14)
6x+15+8x+14
14x+29=225
-29. -29
14x=196
/14. /14
X=14
Fill in 14 for x for each side
13+2(14)
13+28
Side GF: 41 ft
4(14)+2
56+2
Side FE: 58 ft
7(14)
Side DE:98 ft
14+14
Side DG: 28 ft
Hopes this helps please mark brainliest
Fall Math Benchmark
1. For the scenario given, explain in words your process for solving the problem.
Two rectangular walls need to be painted. They are each 12 feet high and 23 feet
wide. It costs $1.50 per square foot for paint. How much will it cost to paint the
walls?
The amount that it will cost to paint the walls, given the cost per square foot and the dimensions of the rectangular walls is $828
How to find the cost?First, find the area of the rectangular walls by the formula for the area of a rectangle which is:
= Length x Width
The area of the rectangles is therefore:
= 12 x 23
= 276 feet ²
The area of the two rectangular walls is:
= 276 + 276
= 552 feet ²
The cost to paint the walls is:
= Area of walls x cost per square feet to paint
= 552 x 1.50
= $828
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(06.02)
Match the verbal expression (term) with its algebraic expression (definition).
Match
Term
A variable cubed
Quotient of some number and three
Product of an unknown value and three
Three less than a variable
Three more than some number
Definition
A) 3a
B) b + 3
C) z + 3
D) y - 3
E) x³
The values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
What is an Expression?
An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Hence the answer is, the statements are:
A variable cubed : x³
Quotient of some number and three: b ÷ 3
Product of an unknown value and three : 3a
Three less than a variable : y-3
Three more than some number : z+3
Hence the answer is, the values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
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What is the slope of a line perpendicular to the line whose equation is 6x + 2y = -32. Fully simplify your answer.
The slope of a line is m=−3
The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
Given that
the slope of 6x+2y=−32:
slope using the standard form:
slope m of a line of the form Ax+By=C equals –A/B
A=6, B=2
m=−6/2
simplify
m=−3
Therefore the slope of a line is m=−3
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Henry drinks 1/2 of a bottle of soda. Sasha then drinks 1/3 of the soda that is left in the bottle. There is now 6 ounces of soda in the bottle. How many ounces of soda were there in the full bottle?
Answer: There were 18 oz. in the full bottle.
Step-by-step explanation:
If there are 6 oz. left, and Sasha drank 1/3 of half the bottle, then that means she drank 3 oz, since 6 is 2/3 of 9, which means that half of the bottle was 9 oz. 9 oz. is half of 18 oz, which means that there were 18 ounces in the full bottle.
Evaluate 1/2x^4 – 3/4x² for x = 2.
Answer:
[tex]-\frac{5}{32}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2(2)^4}-\frac{3}{4(2)^2} \\\frac{1}{32} - \frac{3}{16} = -\frac{5}{32}[/tex]
13) You have $80 and your sister has $160. You are saving
$7 per week and your sister is saving $5 per week. In
how many weeks you and your sister will have the same
amount of money? Write an equation and solve.
Answer: 30 weeks
Step-by-step explanation:
let w = number of weeks
you have = 60 + 7w
she has = 120 + 5w
60+7w = 120 + 5w
7w-5w = 120-60
2w = 60
w = 30 weeks
A rectangular dining room has a perimeter of 24 meters. Its area is 35 square meters. What are the dimensions of the dining room? IN NEED ASAP CLASS IS ABOUT TO END
The dimensions of the rectangle which form the dining room is 7 by 5 meters.
The perimeter of the rectangle is 24 meters.
The total length of a shape's boundaries is its perimeter. The total lengths of all other edges and sides are added to find a shape's perimeter.
Let the length be a and the width be b.
Hence 2(a + b) = 24
or, a+b = 12
Now the area of the rectangle is given as 35 square meters.
Therefore ab = 35
now we will use these two equations to find the dimension of the rectangle
a+b = 12
or, a = 12 - b
again:
ab = 35
or, (12 - b)b = 35
or, 12 b - b² = 35
or, - b² +12b -35 = 0
or, b² - 12b + 35 = 0
or, (b-7) (b-5) = 0
either b = 7 or b = 5 .
Therefore the value of a from the equations is 5 or 7.
Therefore the dimensions of the dining room are 7 by 5 meters.
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a baseball diamond is a square with side 90 feet. if a batter hits the ball and runs towards first base with a speed of 25 ft/sec, at what speed is his distance from second base decreasing when he is two thirds of the way to first base?
The rate when his distance from second base changes and it is two third of the way to first base is - 13.86 feet/s.
let us consider the following values
distance between batter to Second base = d feet
distance between batter to First base
= x feet
distance between first to second base
= 90 feet
Using the Pythagorean theorem:
d² = x² + 90²
Knowing that the velocity of the bat to first base is 25 ft/s,
the distance x can be written as: x
= 90 - 25t
The equation for is,d² = 90²+(90 -25t)²--(1)
we want to find the rate of change of d.
let it be d' and from implicit differentiation:
2d.d' = 2(90-24t) × (-25)
d' = -50(90 - 25t) / (2d)
d' = -25 (90 - 24t) / d ---(*)
We can determine t and d from the fact that the batter is two third to his first base: d = √90^2 + 60^2 = √1 = 108.2 feet
putting the values of d in (1) we get,
=> 90 - 25t = 60 => 25t = 30 => t = 6/5.
Substitute d' in the formula equation (*)
d' = -25 (90 - 24t) / d = -25(90-30)/108.2
d'= - 13.86
d' = - 13.86 feet/s
negative sign means decreasing distance from second base (as it approaches the first
bases, it approaches the second base).
Hence,The required speed is 13.86 feet/s
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Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs. The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs. What is Mrs. Singh's percent error?
Singh percent error is approximately 13%.
What is percent error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs. The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs.
Therefore, Singh's percent error can be calculated as follows:
percent error = 35 - 31 / 31 × 100
percent error = 4 / 31 ×100
percent error = 400 / 31
percent error = 12.9032258065
percent error ≈ 13%
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If f (x) = 2x2 + 4x − 3, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
The difference quotient for the given quadratic equation is:
d = (2h + 4x + 4)
How to get the difference quotient for f(x)?Here we have the quadratic function:
f(x)= 2x² + 4x - 3
And we want to get the difference quotient that is defined as:
d = ( f(x + h) - f(x))/(h)
Replacing our function there, we get:
d = ( 2(x + h)² + 4*(x + h) - 3 - (2x² + 4x - 3)/h
d = (2x² + 2h² + 4xh + 4x + 4h - 3 - 2x² - 4x + 3)/h
d = (2h² + 4xh + 4h)/h
d = (2h + 4x + 4)
That is the difference quotient.
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Dora is paid a salary of $50,000per year. How much would she be paid if she's weekly
Answer:
about 958 dollars
Step-by-step explanation:
50,000÷52.1429 is about 958 dollars weekly
In just two days it will be seven days after three days before Halloween. What is the date today ?
Answer:
November 2nd
Step-by-step explanation:
Halloween = Oct. 31
3 days before Halloween (Oct. 31) is Oct. 28
7 days after that it is Nov. 4
2 days before is November 2nd
In the function y = |x² - 4|, for
how many values of x does y = 3?
Answer:
4 answers
Step-by-step explanation:
y = |x² - 4|
3 = |x² - 4|
3 = x² - 4 and -3 = x² - 4
3+4=x² - 4 + 4 and -3+4=x² - 4 + 4
7=x² and 1=x²
x=[tex]\sqrt{7}[/tex] and x=-[tex]\sqrt{7}[/tex] since x²=7
x=-1 and x=1 since x²=1
x= -[tex]\sqrt{7}[/tex], [tex]\sqrt{7}[/tex], -1, 1 ==> 4 answers
a) 6x(3x+5)-2x(9x-2)=17
b) 2x(3x -1)-3x(2x+11)-70=0
Answer:
a). 18x+30 - 18x+4=17
18x-18x 30+4 =17
34=17
[tex](a) \: { \pink{ \boxed{ \blue{ \sf{x = \frac{13}{30}}}}}}[/tex]
[tex](b) \: { \pink{ \boxed{ \blue{ \sf{x = -2}}}}}[/tex]
Step-by-step explanation:
[tex](a){ \red{ \sf{6x(3x + 5) - 2x(9x - 2) = 17}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{18x}^{2} + 30x \: { \cancel { - 18x}^{2} + 4 = 17}}}}} [/tex]
[tex]{ \red{ \sf{30x + 4 = 17}}}[/tex]
[tex]{ \red{ \sf{30x = 17 - 4}}}[/tex]
[tex]{ \red{ \sf{30x = 13}}}[/tex]
Divide both the sides by 30 then,
[tex]{ \red{ \sf{ \cancel {\frac{30}{30}}}}}{ \red{ \sf{x} = \frac{13}{30}}} [/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{13}{30}}}}}} [/tex]
[tex](b) { \red{ \sf{2x(3x - 1) - 3x(2x + 11) - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{6x}^{2} - 2x}}}} \: \: { \red{ \sf{ \cancel { - 6x}^{2} - 33x - 70 = 0}}} [/tex]
[tex]{ \red{ \sf{ - 2x - 33x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x = 70}}}[/tex]
Divide both the sides by -35 then,
[tex]{ \red{ \sf{ \cancel {\frac{ - 35}{ - 35}}}x}}= { \red{ \sf{ { - \frac{ \cancel{70} ^{2} } { \cancel{35_{1} }}}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]
in a multiple regression model, which of the following is correct regarding the value of the adjusted r^2?
A. It can be negative
B. It has to be positive
C. It can be larger than 1
D. It has to be larger than the coefficient of multiple determination
The correct option is option (B) .
In a Multiple regression Model , the value of adjusted r-Squared is positive.
Adjusted r-Squared :
Adjusted r-squared is a modified version of r-squared adjusted for the number of predictors in the model. The fitted r-squared increases only if the new term improves the model beyond what would be expected by chance. This is reduced if the predictor happens to not improve the model more than expected.
The formula for r-squared,
Adjusted r-squared= 1 - [ ( 1 -r²)(n-1)/(n-k-1)]
where
N --> number of points in the data sample.
K --> number of independent regressors, i. number of variables in the model excluding or constant.
r²--> Indicates how well a term (data point) fits a curve or line.
r-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%.
100% r-squared means that all movements in the security are completely explained by movements in the index.
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On a straight road, Jorge is 7 kilometers east of Peter, Jason is
10 kilometers west of Juan, and Juan is 13 east of Peter. how
many miles is Jorge from Jason?
Answer:
7x10x13=910=910 kilograms
Step-by-step explanation:
18 POINTS AND WILL MARK BRAINLIEST PLS HELP ME IT WAS DUE LAST WEEK
Answer:
B
Step-by-step explanation:
y intercept is 500 so that is how much was in the tank when it started
And slope is -9 which is the steady decline in water
Hopes this helps
Answer: i'm writeing this so you can mark the other person brainliest
Step-by-step explanation:
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
PLEASE HELP ME I FEEL LIKE THIS SHOULD BE SUPER EASY BUT MY BRAIN CAN NOT RN
Answer:
x = 62
y = 41
Step-by-step explanation:
y + 21 = x
x + y + 77 = 180
2y+77 = 180
2y = 82
y = 41
x = 62
Elaine roll 2 fair dice . What i the probability of both dice howing a prime number
The probability of both the dice showing prime numbers is 1/4.
Prime numbers:
The numbers which have only two factors, one and itself are known as prime numbers.
A dice has 6 faces numbering from 1 to 6.
Prime numbers from 1 to 6 are 2, 3, and 5.
Probability of one dice showing a prime number
= (number of favorable outcomes) / (total number of outcomes)
= 3/6
= 1/2
Probability of two dice showing a prime number = (1/2) x (1/2)
= 1/4
Therefore, the probability of both the dice showing a prime number is 1/4.
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What is the value of (−13)4?
52
−52
28,561
−28,561
if the point D (8. -5) is reflected over the y axis, the coordinates of D would be
If the point D (8. -5) is reflected over the y-axis, the coordinates of D' would be: (-8, -5).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to point D, the coordinates of the vertices of point D' include the following:
(x, y) → (-x, y)
Point D = (8, -5) → Point D' = (-8, -5)
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there are 32 students in categories a and b combined; 24 are in a, and 24 are in b. how many are in both a and b?
The number of students that are in both the Categories A and B are 16 students.
In the question ,
it is given that ,
the total number of students in category A and category B is 32 students .
which is represented as A union B ,
that is n(AUB) = 32 ,
the number of students in category A = n(A) = 24
the number of students in category B = n(B) = 24
we need to find the number of students that are in both category ,
that is n(A∩B) .
we know that ,
n(AUB) = n(A) + n(B) - n(A∩B)
Substituting the values , we get
n(A∩B) = 24 + 24 - 32
= 48 - 32
= 16
Therefore , The number of students that are in both the Categories are 16 students.
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solve the simultaneous equations
y = 2 - x
6x + 5y = 11
x + 2y = 2
2x + y = 1
Answer:
x = 2
y = 0
Step-by-step explanation:
Here are the simultaneous equations:
[tex]y=2-x\\6x+5y=11\\x+2y=2\\2x+y=1\\[/tex]
There are only two unknown values, so only two equations are needed to find the answer. I will use these:
[tex]y=2-x\\x+2y=2[/tex]
Substitute the first equation into the y in the second equation:
[tex]x+2(2-x)=2[/tex]
Simplify
[tex]x+4-2x=2\\x=2[/tex]
Use the value of x to find y in equation 1:
[tex]y=2-x\\y=2-2\\y=0[/tex]
Find the value of the variables in the figure. Explain your reasoning.
The value of the variables in the figure is x = 60 degrees and y = 10 degrees.
From the figure:
x + 120 = 180 (since consecutive interior angles equal to 180)
x = 180 - 120
x = 60 degrees.
3y + 40 + 3x - 70 = 180(since supplementary angles = 180)
3y + 3x - 30 = 180
3(y + x) = 180 + 30
y + x = 210/3
y + x = 70
substitute x value
y + 60 = 70
y = 70 - 60
y = 10 degrees.
Therefore the value of the variables in the figure is x = 60 degrees and y = 10 degrees.
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Boden's account has a principal of $600 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answer:$84
Step-by-step explanation:
$84 dollars because 3.5 percent of 600 is 21 so if we do 21x4=$84 well atleast that't what i think
Shawn had some nickels in a jar. He put 147 nickels in the jar. Now there are 435 nickels in the jar. How many nickels were in the jar at the start?
Responses
A 288288
B 218218
C 312312
D 398398
Answer:
A
288 nickels
Step-by-step explanation:
There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.
435 - 147 = 288
So, there were 288 nickels in the jar at the start.
g if you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
The Confidence interval is (0.85,1.05) which contain the sample proportion for 95%of samples size.
Confidence interval is an interval with a confidence level. Confidence interval is always constructed on basis of sample , p = sample statistic - margin of error to sample statistic + margin of error
Confidence interval for a proportion are calculated using the following formula:
p= ( p' - Z√p'(1-q')/n , p'+ Z √p'(1-p')/n ) ---(1)
where, p' ---> sample proportion for sucess
1-p' -----> sample proportion for failure
Z --> Z-value (statistic value)
n---> sample size
we have given that,
sample size ( n)=850 , sample proportion (p') = 0.95 and population proportion= 0.75
a) mean of sample of proportion is same as poplution proportion i.e 0.75 ..
1 -p' = q' = 0.05
Using the formula for margin of error ,
M .E = Z √ p'q'/n ---(2)
as the Z-value for given proportion is 13.46
putting all values in equation( 2) we get,
M.E = 13.45 √0.95×0.05/850 = 0.1005
Now, we shall calculate the confidence interval for given data
confidence interval (p)
= ( 0.95 - 0.100 , 0.95 + 0.100)
p= ( 0.85 , 1.05)
Hence,confidence interval(CI) is (0.85, 1.05).
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Complete Question:
75% of all credit card users carry a balance from month to month. a. If you randomly select 850 credit card users and will compute the sample proportion that carry a balance from month to month, what is the mean of the sample proportion? b. If you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
Show that there exist a rational number a and an irrational number b such that a^b is irrational.
Answer:
In explanation below.
Step-by-step explanation:
Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.