Answer:
-7, 14
Step-by-step explanation:
We start by writing this in the form $x^2 + bx + c = 0$, so we subtract 98 from both sides of the equation.
This gives us $x^2 - 7x - 98 = 0$. We proceed by factoring $x^2 - 7x - 98$, so we seek numbers that multiply to $-98$ and add to $-7$. We find that $7$ and $-14$ work.
Thus, our equation becomes $(x + 7)(x - 14) = 0$. We can now apply the fact that if the product of two real numbers is zero, then at least one of the real numbers must be 0.
Solving $x + 7 = 0$ and $x - 14 = 0$, we find that the solutions are $\boxed{x =-7~\text{and}~x = 14}$.
The value of the equation is given by x = 14 or x = -7
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - 7x = 98 be equation (1)
Subtracting 98 on both sides of the equation , we get
x² - 7x - 98 = 0
Now , on simplifying the equation , we get
x² - 14x + 7x - 98 = 0
Taking x as the common factor of the equation , we get
x ( x - 14 ) + 7 ( x - 14 ) = 0
On further simplification , we get
( x + 7 ) ( x - 14 ) = 0
Now , the two solutions to the equation is
( x + 7 ) = 0
Subtracting 7 on both sides of the equation , we get
x = -7
( x - 14 ) = 0
Adding 14 on both sides of the equation , we get
x = 14
Therefore , the value of A is 14 or - 7
Hence , the equation x² - 7x - 98 = 0 has the solutions of 14 and -7
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2a2 - ab - 3b2 + 9 when a = 3 and b = 2
2(3^2)−(3)(2)−3(2^2)+9
2(3^2)−(3)(2)−3(2^2)+9
= 9
Split 36 into the ratio 1:2
Answer:
12 : 24
Step-by-step explanation:
sum the parts of the ratio, 1 + 2 = 3 parts
Divide 36 by 3 to find the value of one part of the ratio.
36 ÷ 3 = 12 ← value of 1 part of the ratio , thus
2 parts = 2 × 12 = 24
Thus
36 in the ratio 1 : 2 is 12 : 24
Lilee has an ant farm. The population of ants triple every month. Lilee currently has 100 ants in her farm. Write an equation that models the number of ants that lilee has in her farm
Answer:
100 x 3
Step-by-step explanation:
Well, it's a pretty simple problem.
If she already has 100 ants and it triples every month then, we'd multiply.
Key words like triple, double, twice as much can signal that a problem requires multiplication.
In this case, we'd do 100 x 3
which means that after one month, she'd have 300 ants.
which equation is modeled
Answer:
The answer is B
Step-by-step explanation:
4x (green, left)
-2 (red, left)
=
2x (red, right)
6 (orange, right)
Hope that helps
which ratio is same as 2/3
The ratio 4/6 is the same as 2/3 because they have the same proportion.
To find a ratio that is the same as 2/3, multiply or divide both the numerator and the denominator by the same non-zero number.
1. Multiplying by the same number:
If you multiply both the numerator and the denominator of 2/3 by 2, you get:
= (2 × 2) / (3 × 2)
= 4/6
So, the ratio 4/6 is the same as 2/3.
2. Dividing by the same number:
Divide both the numerator and the denominator of 2/3 by 3, you get:
= (2 ÷ 3) / (3 ÷ 3)
= 2/3
So, the ratio 2/3 remains the same.
In conclusion, the ratio 4/6 is the same as 2/3.
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The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d
Answer:
We have established the following sequence
6, 12, 18,...
The given is the Arithmetic sequence with the nth term
[tex]a_n=6n[/tex]
d = 6 is a common difference.
Step-by-step explanation:
Given the formula
Sₙ = 3n² + 3n
Put n = 1 to determine the sum of the first term
S₁ = 3(1)² + 3(1)
S₁ = 3 + 3
S₁ = 6
As the sum of the first term includes the only first term, so
a₁ = 6
Put n = 2 to determine the sum of the two terms
Sₙ = 3n² + 3n
S₂ = 3n² + 3n
S₂ = 3(2)² + 3(2)
S₂ = 12 + 6
S₂ = 18
as
S₂ = a₁ + a₂
substituting S₂ = 18, a₁ = 6
18 = 6 + a₂
12 = a₂
so
a₂ = 12
Put n = 3 to determine the sum of the two terms
Sₙ = 3n² + 3n
S₃ = 3(3)² + 3(3)
S₃ = 27 + 9
S₃ =36
as
S₃ = a₁ + a₂ + a₃
substitutingS₃ =36, a₁ = 6, a₂ = 12
36 = 6+12+a₃
a₃ = 36-6-12
a₃ = 18
Thus,
a₁ = 6
a₂ = 12
a₃ = 18
Therefore, the sequence becomes
a₁, a₂, a₃,...
6, 12, 18,...
Let us check the common difference 'd' between the adjacent terms
d = 12 - 6 = 6
d = 18 - 12 = 6
As the common difference 'd' between adjacent terms is the same, therefore the sequence is Arithmetic.
Thus,
d = 6Furthermore, the nth term of the Arithmetic sequence can be defined as
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting d = 6 and a₁ = 6
[tex]a_n=6\left(n-1\right)+6[/tex]
[tex]a_n=6n[/tex]
help meeeeeeeeeee its limited
Answer:
2 2/4
Step-by-step explanation:
add the buttons greater then 1 and it will be 2 2/4
Which statement is true for all functions f(x)?
Answer:D
Step-by-step explanation: The graph of -f(x) is the graph of f(x) reflected over the y-axis.
Rachel pays $131.44 for a desk, including tax. the tax is 31 cents less than 1/16 of the desk's price. what is the price of the desk before adding the tax?
help me plz
Please answer this quickly
A question on a test asks students to find the speed at which a car travels. The graph shows a proportional relationship between the distance traveled in miles and time in hours. billy incorrectly says that the speed of the car is 1/62
mile per hour. What is the speed of the car? What error might billy have made?
Answer: For time t ≥ 0 hours, let r(t) = 120 1 − e−10t2 represent the speed, in kilometers per hour, at which a ()
car travels along a straight road. The number of liters of gasoline used by the car to travel x kilometers is −x 2
modeled by g(x) = 0.05x 1 − e . ()
(a) How many kilometers does the car travel during the first 2 hours?
(b) Find the rate of change with respect to time of the number of liters of gasoline used by the car when
t = 2 hours. Indicate units of measure.
(c) How many liters of gasoline have been used by the car when it reaches a speed of 80 kilometers per
(a)
(b)
hour?
∫ 2 r (t ) dt = 206.370 kilometers 0
dg dg dx dx dt=dx⋅dt; dt=r(t)
2 : {1 : integral 1 : answer
3:{2:useschainrule
1 : answer with units
dg dt
t=2
dg
= dx ⋅r(2)
x=206.370
= (0.050)(120) = 6 liters hour
(c)
Let T be the time at which the car’s speed reaches 80 kilometers per hour.
Then, r(T ) = 80 or T = 0.331453 hours. At time T, the car has gone
x(T ) = ∫ T r (t ) dt = 10.794097 kilometers 0
and has consumed g(x(T )) = 0.537 liters of gasoline.
Select the Correct answer.
I can't see anything it is full black
Need help ASAP!!
Find the unknown side of the triangle below (round to the nearest tenth).
A.) 210.5 cm
B.) 5.4 cm
C.) 16 cm
D.) 20.5 cm
Answer:
the answer is D, 20.5cm
Step-by-step explanation:
x is hypotenuse
hypotenuse formula:
[tex]hypotenuse = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
let 15cm = a
let 14cm = b
[tex]x = \sqrt{15 {}^{2} + {14}^{2} } [/tex]
[tex]x = \sqrt{225 + 196} [/tex]
[tex]x = \sqrt{421} [/tex]
[tex]x = 20.5cm[/tex]
find the midpoint, multiple choice question
Answer:
(-2,-1)
Step-by-step explanation:
Ive done a lot of these problems before, hope this helps
What adds to give -14 but multiplies to give 48?
Answer:
6
Step-by-step explanation:
Answer:
-6 and -8
Step-by-step explanation:
-6+(-8)=-14
-6(-8)=48
It made me reload lol
The local car dealership has noticed a 3:1
ratio for people purchasing SUV's to those
purchasing trucks. If they have room for
128 trucks and SUV's on their lot, how
many trucks should they have available to
sell?
Answer:
32 trucks.
Step-by-step explanation:
3:1
Every time 3 SUV's are sold, one truck is sold. This would also mean that [tex]\frac{3}{4}[/tex] of both trucks and SUV's sold are SUV's. If we divide 128 into fourths, then you get 32. One fourth of 128 is 32. So, they should have 32 trucks (and 96 SUV's)
POSSIBLE PC
This graph shows the height of Ms. Pendleton's cat, Mac, as she climbs around the house.
n
1
7
8
2 3 4 5 6
time (seconds)
Which sentence describes the point f (6) = 2 ?
O After 6 seconds, Mac's height is 2 meters.
O After 2 minutes, Mac's height is 6 meters.
O After 2 seconds, Mac's height is 6 meters.
O After 6 seconds, Mac's height is 2 feet.
Find the slope-intercept equation of the line that
passes through (0, 2) and has a slope of 1/2
Answer:
1/2
Step-by-step explanation:
What's the nth term of the following question:
−
5
,
−
7
,
−
9
,
−
11
,
−
13
Answer:
-21
Step-by-step explanation:
-13 +(-2) = -15
-15+(-2) = -17
-17+(-2 )=- 19
-19+ (-2)= -21
Please help ✨yeahhh
Answer:
b
Step-by-step explanation:
exposed clout chaser
46.798 divided by 9.086
Answer:
5.1505613031
Step-by-step explanation:
hope it helps!
Answer:
5.1505613031
Step-by-step explanation:
Hope this helped have an amazing day!
Based on the scatter plot below, what is the most likely value for "Pounds of Apples" when "Number of Apples" is 80?
A. 42
B. 81
C. 158
D. 398
Help me quickly please!!!
Answer:
c hope this help
Step-by-step explanation:
Answer:
It’s A. 42
Step-by-step explanation:
The dimensions of a sports pennant are given in the diagram. Find the values of x and y.
x=
y=
Answer:
x = 79°
y = 22°
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°
79° + x° + y° = 180° the given triangular shape is isosceles which means x = 79°
so 79° + 79° + y° = 180° add like terms
158° + y° = 180° subtract 158 from both sides
y° = 22°
Answer:
x=79
y=22
Step-by-step explanation:
its an isosceles triangle meaning that 2 sides are the same and if 2 sides are the same 2 angles are and that means that 79 would have to equal x because that is the one side and then you add the two 79s to get 158 and subtract that minus 180 to get 22 leaving that to be y
79+79=158
180-158=22
y=22
I tought of a number double it then added 3. The result multiplied by 4 came to 52,what was the number I tought of?
Answer:
5
Step-by-step explanation:
double 5 is 10
10+3=13
13 multiplied by 4=52
Input Output Which ordered pair needs to be removed in order for the mapping to represent a function? -3 4 O (-3, 4) O (-2, -1) O (1, -3) 0 2 -2 O (3,7) -3 →_1 3 7
Answer:
Acording to my brain the answer is (-2,-1) In other Words The correct answer is Option B
Step-by-step explanation:
God Bless :)
The ordered pair that needs to be removed in order for the mapping to represent a function is either: (-2, -1) or (2, -2).
What is a function?The term "function" refers to a relationship between a set of inputs and outputs. Just one output is connected to each input in a function, which connects inputs in that manner. Every function has a domain, co-domain, and range.
To represent a function, each input (x-value) must be associated with only one output (y-value). Therefore, in order for the mapping to represent a function, we need to remove any ordered pairs that violate this rule.
Looking at the options given, we can see that only one option has a repeated x-value:
O (-2, -1) and 0 (2, -2)
Both of these ordered pairs have the same x-value (either -2 or 2), but different y-values. This means that they violate the rule that each input must be associated with only one output.
Therefore, the ordered pair that needs to be removed in order for the mapping to represent a function is either:
O (-2, -1)
or
0 (2, -2)
We need to remove one of these ordered pairs to make the mapping a function.
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What are the correct answers?
Which point below is a solution to the equation y = 2x + 3?
A (145, 291)
B (78, 163)
C (37, 77)
Answer:
C (37, 77)
Step-by-step explanation:
Option A:[tex]291=2(145)+3\\\\291=290+3\\\\\boxed{291\neq 293}[/tex]
Option A is not a solution.
Option B:[tex]163=2(78)+3\\\\163=156+3\\\\\boxed{163\neq 159}[/tex]
Option B is not a solution.
Option C:[tex]77=2(37)+3\\\\77=74+3\\\\\boxed{77=77}[/tex]
Option C is a solution.
Hope this helps.
Answer:
C
Step-by-step explanation:
To determine which point is a solution, substitute the x- coordinate into the equation and if the value is equal to the y- coordinate then it is a solution
A (145, 291 )
y = 2(145) + 3 = 290 + 3 = 293 ≠ 291 ← not a solution
B (78, 163 )
y = 2(78) + 3 = 156 + 3 = 159 ≠ 163 ← not a solution
C (37, 77 )
y = 2(37) + 3 = 74 + 3 = 77 ← solution to the equation
plzz help me it is hard plz
Answer:
LETS GO WITH B
Step-by-step explanation:
On Saturdays, Eve earns $14 per hour for yard work and an extra amount for dog walking. Look at the table. Choose the linear function f Eve can use to determine her pay.
Hours 1 2 3 4 5
Pay 26 40 54 68 82
A. f(x) = x + 14
B. f(x) = 12x + 16
C. f(x) = 12x + 14
D. f(x) = 14x + 12
The linear function f Eve can use to determine her pay would be; D. f(x) = 14x + 12
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is the form Ax + B = 0.
Given that Eve earns $14 per hour for yard work and an extra amount for dog walking on Saturdays.
The table shows the data;
Hours 1 2 3 4 5
Pay 26 40 54 68 82
Thus, the linear function f Eve can use to determine her pay is;
f(x) = 14x + 12
To check;
f(x) = 14x + 12
f(x) = 14(1) + 12
f(x) = 14 + 12 = 26
Hence, The linear function f Eve can use to determine her pay would be; D. f(x) = 14x + 12
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