Answer:
(- 5, - 3 )
Step-by-step explanation:
Given the 2 equations
- 3x + 10y = - 15 → (1)
5x - 7y = - 4 → (2)
Multiplying (1) by 5 and (2) by 3 and adding the result, eliminates the x- term.
- 15x + 50y = - 75 → (3)
15x - 21y = - 12 → (4)
Add (3) and (4) term by term to eliminate x, that is
29y = - 87 ( divide both sides by 29 )
y = - 3
Substitute y = - 3 into either of the 2 equations and solve for x
Substituting into (1)
- 3x + 10(- 3) = - 15
- 3x - 30 = - 15 ( add 30 to both sides )
- 3x = 15 ( divide both sides by - 3 )
x = - 5
solution is (- 5, - 3 )
The function Q(x)=2x^2-kx+18. For what value of k does Q(x) have one distinct real solution? (NEEDS TO BE DONE WITHIN 2 HOURS!)
Answer:
k = 12
Step-by-step explanation:
Given:
The equation [tex]Q(x)=2x^2-kx+18[/tex]
To find:
Value of [tex]k = ?[/tex] for which the given equation has one distinct real solution.
Solution:
The given equation is a quadratic equation.
There are always two solutions of a quadratic equation.
For the equation: [tex]ax^{2} +bx+c=0[/tex] to have one distinct solution:
[tex]b^2 - 4ac = 0[/tex]
Here,
a = 2,
b = -k and
c = 18
Putting the values, we get:
[tex](-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12[/tex]
The equation becomes:
[tex]Q(x)=2x^2-12x+18[/tex]
And the one root is:
[tex]2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3[/tex]
Jared cycles 3/4 miles in 5 minutes. Roy cycles 2 miles in 13 minutes. Whose speed is greater
Answer:
Roy speed is greater
Hope this helps
Answer:
Roy
Step-by-step explanation:
(3/4)/5 = 0.15 so Jared cycles 0.15 miles per minute
2 / 13 = 0.15384... so Roy cycles about 0.154 miles per minute
Roy cycles faster
An angle's measure is 43 less than 6 times the measure of its
complement. Find the measure of both angles,
Step-by-step explanation:
A = 6(90-A)-43 Simplify and solve for A.
A = 540-6A-43
A = 497-6A Add 6A to both sides.
7A = 497 Divide both sides by 7.
A = 71 degrees
The complement of A = 90-A = 09-71 = 19
Hope this help :)
...............................................
Answer:
3p = 1/2
Step-by-step explanation:
Left side: 3pRight side: 1/2Because they're balanced, the right and left side are equaledSo, 3p = 1/2I hope this helps!
How can you use the Quotient of Powers, Power of a Quotient, Identity Exponent and Zero Exponent Laws to evaluate numerical expressions with whole-number exponents?
While dealing with laws of exponents, exponents should be subtracted when splitting exponential formulas with the same base.
Use the Quotient of Powers Rule to reduce the number of terms when splitting like terms with exponents. According to this rule, to determine the solution while dividing terms with the same base, simply remove their exponents. The trick is to only take out exponents with matching bases.
Exponents are added when two powers of the same base are multiplied. Therefore, the exponents are subtracted when two powers of the same base are divided. To put it another way, abac=ab + c is true for all real numbers a, b, and c.
It is so established that any integer or phrase raised to the power of zero always equals 1. To put it another way, the outcome is 1 if the exponent is 0. A 0 = 1 and (a/b) 0 = 1 create the general version of the zero exponent rule.
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A ball is thrown straight up from the top of a building that is 280 feet high with an initial velocity of 48 ft/s. The height of the object can be modeled by the equation s(t)=−16t2+48t+280.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation. Then, determine the time.
Answer:
i hope it helpful
thank you
Answer:
Answer in interval notation is (3, 5.94].
Step-by-step explanation:
First find the time that the ball is level with the top of the building on its descent. You can do this by solving 280 = -16^2 + 48t + 280 for t. This gives t = 3 seconds .
Then when the ball reaches the ground the time t is obtained by solving 0 = -16t^2 + 48t + 280 This gives t = 5.94
seconds.
Answer in interval notation is (3, 5.94].
PLEASE HELP I WILL GIVE BRAINLIEST!
the answer is the second one
Step-by-step explanation:
y=mx+c where m is the gradient or slope and c is the y intercept I think this is right
5
The average rate of change of g(x) between x = 4 and x = 7 is Ē. Which statement must be true?
Answer:
c. 5/6 = [ g(7) − g(4) ] / (7 − 4)
Step-by-step explanation:
Given the definitions of f(x) and g(x) below, find the value of g(ƒ (0)).
f(x) = 3x²+x-6
g(x) = -4x - 3
Value of g(ƒ (0)) =18 .
Definitions of f(x) and g(x) -
Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”. The function g (x) is called an inner function and the function f (x) is called an outer function.
The composition (g ° f)(x) means "evaluate f at x, then evaluate g at the result f(x)". The product (g*f)(x) means "evaluate g and f at x and multiply the results".
An algebraic function is a function that involves only algebraic operations. These operations include addition, subtraction, multiplication, division, and exponentiation.
given
f(x) = 3x²+x-6
g(x) = -4x - 3
find the value of g(ƒ (0))
g(ƒ (0)) = ?
g( f(x) ) = 3 ( f(x) )² +( f(x) )−6
Now, replace every f(x) on the right side with the function you entered in for f(x) :
g(f(x)) = 3( f(x) )² +( f(x) )−6
⇓
g(f(x)) = 3( −4x−3 )² +( −4x−3 )−6
Simplify the expression.
g(f(x)) = 3(−4x−3)² +(−4x−3)−6
= 3(−4x−3)² − 4x−9
So, g(f(x))=3(−4x−3)² −4x−9.
g(ƒ (0)) = 3(−4× 0 −3)² −4× 0−9
g(ƒ (0)) = 3(−3)² −9
g(ƒ (0)) = 3 × 9 −9
g(ƒ (0)) = 27 − 9
g(ƒ (0)) =18 .
Hence, by using the definitions of f(x) and g(x) the value of g(ƒ (0)) =18.
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how do i express this as a trinomial
(2x+5)(3x+7)
Answer:
6x^2 + 29x + 35
Step-by-step explanation:
(2x+5)(3x+7)
multiply 2x with 3x and 7
multiply 5 with 3x and 7
simplify
6x^2 + 14x + 15x + 35
= 6x^2 + 29x + 35
according to the fundamental theorem of algebra, how many roots exist for the polynomial function? (9x 7)(4x 1)(3x 4)
3 number of roots exist for the polynomial function.
Step-by-step explanation:
As we know that the polynomial can only have exact number of roots as high as the degree of that polynomial is.
We can also prove it. Assume there is a polynomial
(x+2)(x+3) =0
Here the degree of the polynomial is 2 and the number of possible solutions are also 2. As it is evident that x is either equal to -2 or -3.
From the given condition,
(9x + 7)(4x + 1)(3x + 4)
we know that the degree of the polynomial is 3 because after expansion it becomes,
108x^3 + 255 x^2 +169x + 28 =0
Since, highest power of the variable is 3. Its degree is 3.
Therefore, possible number of roots that exist for the polynomial function are 3.
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If both lines had been dotted lines instead, how might that have affected the possible solutions?
Answer:
Step-by-step explanation:
You will have less possible solution y is less than or y is greater than so everything touching the line will not be a solution just everything else.
What is the image point of (-1, -3) after
By using the translation formula, the image point of (- 1, - 3) is equal to the point (2, 1).
How to determine the coordinates of the image of a point by using a translation formula
In this problem we find the coordinates of a point, whose image must be found by using a translation, a kind of rigid transformation. The formula for the determination of the coordinates of the image is introduced below:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorIf we know that P(x, y) = (- 1, - 3) and T(x, y) = (3, 4), then the coordinates of the resulting point according to the transformation rule are:
P'(x, y) = (- 1, - 3) + (3, 4)
P'(x, y) = (2, 1)
The image point of (- 1, - 3) is equal to the point (2, 1).
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the product of a number and -7 is 63."
Answer:
the number is -9
Step-by-step explanation:
Use the number line below, where RS=5y+5, ST=2y+5, and RT=52. a. What is the value of y? b. Find RS and ST.
Answer:
y = 6, RS = 35 and ST = 17
Step-by-step explanation:
Given that,
RS = 5y+5
ST = 2y+5
RT = 52
If we consider a number line,
RT = RS + ST
52 = 5y+5 + 2y+5
52 = 7y + 10
7y = 52-10
7y = 42
y = 6
RS = 5y+5
= 5(6)+5
= 35
ST = 2y+5
= 2(6) +5
= 17
Hence, this is the required solution.
Angle 4 = 104 degrees Angle 6 = (2x - 4) degrees Solve for x.
Answer: x = 40
Step-by-step explanation:
104 + 2x -4 = 180
104 - 4 + 2x = 180
100 + 2x = 180
2x = 180 -100
2x = 80
x = 80/2
x = 40
2.3.4 - What two numbers multiply to -40 and add up to -3?
Your answer
Is it 120
Answer:
-8 and 5
Step-by-step explanation:
HELPPP ASAP PLZZZ!!!!!
Answer:
its c
Step-by-step explanation:
why do I need to explain
ANSWER QUICKLY WILL MARK BRAINLIEST
Solve this equation and show all your work
-5 x 2 ÷ -2
Answer: The answer is <5>
Step-by-step explanation:
Solution Steps
−5×2÷−2
Cancel out −2 and −2.
−5(−1)
Multiply −5 and −1 to get 5.
5
I hope this helps!
Enter the equation of the line in slope-intercept form.
Slope is -1, and (2,5) is on the line.
The equation of the line isy =
Answer:
-x+7
Step-by-step explanation:
y-5= -1(x-2)
y-5= -1x+2
+5 +5
y= -x+7
Evaluate square root of 121
Answer:
the square root of 121 is 11
I need to find x, please
This is the last question number 10 please help me and have a good night and be safe out there and please wear a MASK!!!❤️
Answer:
First choice, 75%
Step-by-step explanation:
Add all the numbers together:
15 + 8 + 10 + 12 + 15 = 60
So the probability that you'll get a lose a turn card is 15/60 which simplified is 1/4, 1/4 in decimal form is 0.25 which is 25%. % means out of 100 so to double check: 1/4 times 100 = 100/4 = 25%
There's a 25% chance that you will draw the lose a turn card so
100% - 25% = 75%
So there's a 75% probability you will not draw the lose a turn card
2 1/2 times 5 please answer!!
Answer:
12.5
Step-by-step explanation:
2 1/2 is the same as 5/2
(2*2 = 4 +1 = 5, so the mixed number 2 1/2 turns into 5/2)
so 5/2 * 5 = 5/2 * 5/1 = 25/2 = 12.5
13) The value of x for which 3(x-1) = 4(x-5) is
Answer:
The value of x=17.
Step-by-step explanation:
3(x-1) = 4(x-5)
=3x-3=4x-20
Subtract both sides by 4x.
=3x-3-4x=4x-20-4x
= −x−3=−20
Add 3 to both sides.
=−x−3+3=−20+3
−x=−17
Divide both sides by -1.
−x/-1=−17/-1
x=17
how many 3 digit numbers can be formed using numerals in the set {3,2,7,9} if repetition is not allowed
Heather buys a dog bowl priced at $8. If the sales tax is 10%, how much tax will Heather
pay?
Answer:
I think the answer is 2 dollars
Step-by-step explanation:
Which set of numbers is correctly ordered from greatest to least?
Answer:
It's the last choice.
Step-by-step explanation:
Convert them to decimal form:-
7 1/3 = 7.333....
221/30 = 7.36666......
⁻⁻⁻⁻⁻
7.36 = 7.36363636,,,
2.4√(3π) = 7.367952297
So, from greatest to least they are:
___
2.4√(3π), 221/30, 7.36, 7 1/3.
Liz wants to buy a shirt for $25.what will the total cost after tax be if Liz buys the shirt in Springfield
Answer:
ya
Step-by-step explanation:
Sam noticed that some people purchased like items and decided to start offering a bundle. If you buy the following items together, you get 15% off. How much will the bundle cost? $11.00 snorkle $30.00 for goggles $36.00 for flipperd
Answer: $65.45
Step-by-step explanation:
Cost of Snorkle = $11.00
Cost of goggles = $30.00
Cost for flippered = $36.00
Total cost = $11.00 + $30.00 + $36.00 = $77.00
Since there's a 15% off, the cost of the bundle will be:
= $77 - (15% × $77)
= $77 - (0.15 × $77)
= $77 - $11.55
= $65.45