Answer:
x=3, y=7
x=-2, y=2
Step-by-step explanation:
System of Equations
We have the following equations:
[tex]y=-x^2+2x+10[/tex]
[tex]y=x+4[/tex]
We'll solve it by substitution. Since the second equation is already solved for y, we use that expression and substitute into the first equation:
[tex]x+4=-x^2+2x+10[/tex]
Since this is a quadratic equation, it's convenient to have all terms to one side:
[tex]x+4+x^2-2x-10=0[/tex]
Simplifying and reordering:
[tex]x^2-x-6=0[/tex]
Factoring:
[tex](x-3)(x+2)=0[/tex]
Solving:
x=3, x=-2
Those yield to two solutions for y:
y=x+4
y=7, y=2
The solutions of the system are:
x=3, y=7
x=-2, y=2
Match the number with its opposite.
Match Term Definition
9.2 A) 2.9
−2.9 B) −9.2
−1.4 C) −4.1
4.1 D) 1.4
Answer:
9.2 - B
-2.9 - A
-1.4 - D
4.1 - C
Step-by-step explanation:hope this helps
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 36 x2 x dx
We need to find the integration of (36x²)x.dx .
We know,
[tex]\int x^n.dx = \dfrac{x^{n+1}}{n+1} +c[/tex]
Now,
[tex]I=\int {36x^2x} \, dx \\\\I=36\int x^3.dx\\ \\I=36\times \dfrac{x^4}{4}+c\\\\I=9x^4+c[/tex]
Therefore, the integration of (36x²)x.dx is [tex]9x^4+c[/tex] .
Hence, this is the required solution.
Use the multiplier method to increase £72 by 12%
You must show your working.
Answer:
£80.62
Step-by-step explanation:
100+12%=112%
112/100= 1.12
1.12*£72 =£80.62
Evaluate −b2−2bx2−x when x=−2.
An expression is defined as a set of numbers, variables, and mathematical operations. The value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the expression −b²−2bx²−x will be,
−b² − 2bx² − x
= − b² − 2b(-2)² − (-2)
= − b² − 8b + 4
Hence, the value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
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10times larger than 40
Answer:400
Step-by-step explanation:10×40=400
Answer:400
Step-by-step explanation:
match the simplified expressions to an equivalent expression
Spencer is 10 years old. His age is two years less than three times his sister's age. How old is Spencer's sister?
The age of Spencer's sister is 4 years old.
What is an Equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Spencer is 10 years old. His age is two years less than three times his sister's age.
Let the age of Spencer's sister be x
According to the question,
3x - 2 = 10
3x = 10 +2
3x = 12
x = 12/3
x = 4
Hence, The age of Spencer's sister is 4 years old.
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priya changed the rate at which flowed through the faucet. write an equation that represents the relationship w of t and when it takes 3 minutes to fill the cooler with 1 gallon of water. Which of the following equations represent the relationship between w and t? select all that apply.
Answer:
i love you sm
Step-by-step explanation:
Taylor is driving on the freeway at 55 miles per hour. What question finds her distance
Answer:
distance(miles) = number of hours driven * 55
Step-by-step explanation:
PLEASE HELP
Logan bought a baseball bat on a trip. The baseball bat is 29 inches long.
Logan thinks he can bring the baseball bat home in his suitcase. Is he correct? Use your understanding of the Pythagorean Theorem to explain your answer.
Answer:
Use a^2 + b^2 = c^2 and substitute
18^2 + 24^2 = c^2
Solve what we know
324 + 576 = c^2
324 + 576 = 900
Square root 900 to get C
sqrt of 900 equals 30
So, yes he can fit the baseball bat in his suitcase
A 2 1/2 pound bag of grass seed covers 1/8 of an acre. How much grass seed is needed for 1 acre?
Answer:
it needs 234 grass seeds for the acre
For a statistics project a community college student at Diablo Valley College decides to investigate cheating in two popular majors at DVC: business and nursing. She selects a random sample of nursing and business courses and convinces the professors to distribute a short anonymous survey in their classes. The question about cheating is one of many other questions about college life.
When the student summarizes the data, she finds that 42 of the 50 business students and 38 of the 70 nursing students admitted to cheating in their courses. Can the student proceed with the calculation of the confidence interval for the difference in population proportions?
Answer:
The student can proceed with the calculation of the confidence interval for the difference in population proportions. This is because, from the data she has, 3/4 of the Business students admitted to cheating while 1/2 of the Nursing students admitted to cheating also.
This is above the average number of students in her given sample size which is valid for extrapolation to the College Majors being investigated.
Step-by-step explanation:
W/4 -4=3
Solve the eqution pls!
Answer:
W=28
Step-by-step explanation:
(W/4)-4=3
(W/4)=7
W=28
what is the range of y= square root of x+5
Answer:
Range: [5,∞),{y|y≥5}
Step-by-step explanation:
Set the radicand in √x greater than or equal to 0 to find where the expression is defined.
x≥0
the domain is all values of X that make the expression defined.
Interval Notation:
[0,∞)
Set-Builder Notation:
{x|x≥0}
The range of an even indexed radical starts at its starting point (0,5) and extends to infinity.
Interval Notation:
[5,∞)
Set-Builder Notation:
{y|y≥5}
Determine the domain and range.
Domain: [0,∞),{x|x≥0}
Range: [5,∞),{y|y≥5}
I hope this helps you. Sorry if it doesn’t!!!!
To make the expression 4x−2+□(2x+4) equivalent to 2(6x+7), what must be the value in the box? PLSSSSS HELLPPP
Answer:
4 goes in the box
Step-by-step explanation:
The solution of the equation 4x − 2 + y(2x + 4) = 2(6x + 7) will be 4.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let the value inside the box be 'y'. Then the equation is given as,
4x − 2 + y(2x + 4) = 2(6x + 7)
Simplify the equation, then we have
4x − 2 + y(2x + 4) = 2(6x + 7)
4x − 2 + y(2x + 4) = 12x + 14
y(2x + 4) = 8x + 16
y = 4(2x + 4) / (2x + 4)
y = 4
The solution of the equation 4x − 2 + y(2x + 4) = 2(6x + 7) will be 4.
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Add and subtract the rational expressions.
Which statements are true about the process for adding and subtracting the rational expressions? Check all that apply. The expression is not defined when t = 0. The first step is to use the order of operations and simplify the expression inside the parentheses. The denominator will be simplified to 15t. The numerator will be simplified to 13t 8. The numerator will be simplified to 13t 2
Answer:
The numerator will simplified to 13t-2
Step-by-step explanation:
After you write the numerators with the common denominator, you collect like terms and then calculate.
Answer:
A , B , E
Step-by-step explanation:
Correct on edge 2021. Just did the assignment.
Have a good day <3
2d + 7 = 9
Hellllllpppppp
Answer:
Doesn't 2+7 = 9 itself?
Step-by-step explanation:
Evaluate 2x+6y when x= -4/5 and y= 1/3 Write your answer as a fraction or mixed number in simplest form.
2/5 is a answer
in this we can se the answer is 2/5
If you multiply a matrix and its inverse together, you will always get the identity
matrix.
True
False
Answer:
True
Step-by-step explanation:
If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I. And the point of the identity matrix is that IX = X for any matrix X (meaning "any matrix of the correct size", of course).
Answer:
Yes
Step-by-step explanation: And 1 is the identity, so called because 1x = x for any number x. It works the same way for matrices. If you multiply a matrix (such as A) and its inverse (in this case, A–1), you get the identity matrix I.
Find the surface area of a triangular prism that has a height of 11 meters and the following triangular base. All
dimensions are in meters.
13.5
4
surface area =
m?
Answer:
3 is your answer took the test
Step-by-step explanation:
Answer:
S A = 146 m^2
Step-by-step explanation:
2.
Fifty people who watch television were recently
polled as to which type of program they preferred.
The results are shown in the table.
Television Survey
Type of Show Number
who watch
comedy
16
documentary 9
drama
12
musical
8
news
5
What percent of those surveyed preferred to watch
comedy shows?
Answer:
39.02%
or
39%
Step-by-step explanation:
A can of fruit contains 411 grams. One gram is approximately 0.035 ounces. About how many ounces does the can contain?
Answer:
14.385 ounces
Step-by-step explanation:
Converting grams to ounces:
1g ----- 0.035 ounces
411g ----- ?
Since we multiply 411 to the left hand side, multiply the left hand side by 411 too.
411g
= 0.035(411) ounces
= 14.385 ounces
Thus, the can contains 14.385 ounces of fruit.
Name an equivalent ratio for One-half with a denominator of 8.
a. 4 Over 8
c. 5 Over 8
b. 1 Over 8
d. 3 Over 8
Answer:
it is A
Step-by-step explanation:
You are a school photographer taking individual and class pictures for 2 classes of 21 students each. On average, each individual picture takes 3 minutes and a class picture takes 10 minutes.About how long should it take you to get all of the pictures
Answer:
2h and 26 minutes
Step-by-step explanation:
21x2=42
42x3=126
2x10=20
126+20=146
146m=2h 26m
q(x) = –2x+1
r.(x)=x²+2
Find the value of q (r (3)).
A food scientist determine the new type of orange is 15.38 mg of vitamin c/oz how much vitamin C is in orange that weighs 6 3/5 oz in your answer as a decimal to the nearest 10th in the box
Answer:
(Sorry this is a late response) This fraction 6 3/5 would equal 6.6 so 6 3/5=6.6 Then you will do 6.6 times 15.38=101.508 or 101.5
Step-by-step explanation:
You would divide 3 and 5 or 5 and 3 because 3 and 5 equals the fraction 3/5. The dividend is 3 and the 5 is the divisor. The quotient of this is 0.6. So the next step would be to add the 6 from 6 3/5 so this is the whole number so add it in front of 0.6 so it would turn into 6.6. The last step is to multiply the weight of the orange by the mg of vitamin C/oz that is 15.38 so multiply 6.6 by 15.38 this would equal 101.508 so you would just round this to a better answer and that would make it 101.5. I hope this helps :0
FIRST RIGHT GETS BRAINLIEST
Answer:
-1 + 7 =-8
Step-by-step explanation:
Answer:
-6, -7
Step-by-step explanation:
-1 + -6 = -7
3 + 8 + 6 + 6 + 6 = 58 + 6
How do we solve this
Answer:
93
Step-by-step explanation:
Find the solution to the equation.
4(x + 7) = 38 i need it ASAP plzzz
Answer:
x = 2.5
or
x = 1/4
Step-by-step explanation:
watch the following steps:
4x + 28 = 38
4x = 38 - 28
4x = 10
x = 2.5
or
x = 1/4
Pls consider marking my answer as Brainliest! It would mean a lot!
Answer:
2.5, maybe
Step-by-step explanation:
distribute 4 into x and 7
subtract 28 from both sides (28-28, 38-28)
divide 4 and 10
2.5
it seems odd...
A food truck sells tacos $1.25 a piece. The truck operator earned $360.00 last night.
How many tacos did the food truck sell last night?
28.8 tacos
288 tacos
300 tacos
2.88 tacos
Answer:
288
Step-by-step explanation:
Each taco is 1.25 dollars and you are trying to figure out how many tacos he sold to do this we make an equation.
Step 1
1.25 x = 360
x =is the amount of tacos sold.
Step 2
1.25 x = 360
/1.25 /1.25
to get x on its own we need to cancel out the 1.25 so we dived because it was multiplied to the x. we did the same on the other side to balance the equation.
Step 3
x = 288
we now need to identify what x is, we can see it is 288. If we trade x for what it means it is then this is your answer the amount of tacos sold=288
i hope this helps ;)