Answer:
[tex]x_1=-4\\\\x_2=\frac{1}{3}[/tex]
Step-by-step explanation:
Given the quadratic equation:
[tex]2x^2+14x-4=-x^2+3x[/tex]
You can follow these steps in order to solve it:
- Make the equation equal to 0:
[tex]2x^2+14x-4+x^2-3x=0[/tex]
- Now, add the like terms:
[tex]3x^2+11x-4=0[/tex]
- Finally, apply the Quadratic formula ([tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]):
In this case we know that:
[tex]a=3\\b=11\\c=-4[/tex]
Therefore, substituting values into the Quadratic formula and evaluating, we get:
[tex]x=\frac{-11\±\sqrt{11^2-4(3)(-4)} }{2(3)}\\\\x_1=-4\\\\x_2=\frac{1}{3}[/tex]
To find the solutions to the quadratic equation 2x^2+14x-4=-x^2+3x, we need to rearrange the equation and use the quadratic formula.
Explanation:The quadratic equation is 2x^2+14x-4=-x^2+3x. To find the solutions, we need to rearrange the equation in the form ax^2 + bx + c = 0. Combining like terms, we get 3x^2 + 11x - 4 = 0. Now we can use the quadratic formula to find the solutions:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values a = 3, b = 11, and c = -4 into the formula, we can calculate the solutions.
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How much of 10% HCl and 35% HCl would be needed to mix and produce 60 liters of 25% HCl?
About 30 & 30 liters
About 33 & 27 liters
About 36 & 24 liters
About 39 & 21 liters
Answer:
Equation:
HCL + HCL = HCL
0.30x + 0.45(50-x) = 0.35*50
Multiply thru by 100 to get:
30x + 45*50 - 45x = 35*50
-15x = -10*50
x = (2/3)50
x = 33 1/3 liters (amt. of 30% solution needed in the mixture)
50-x = 16 2/3 liters (amt. of 45% solution needed in the mixture)
=============
Step-by-step explanation:
Answer:
about 36 and 24 liters
Step-by-step explanation:
a+b = 60 1
let A multiplied by 10 percent and B multiplied by 35 percent then
10 a + 35 b = 1500 ( 60 * 25 ) 2
add no. 1 to 2 and multiply no.1 by -10
-10 a+ -10 b = -600
10 a+ 35 b = 1500 adding
then 25 b = 900 then b = 36 liter
then a = 24 liter
1,580 milliliters (mL) is equal to how many liters (L)?
For this case we must make a conversion. By definition, we have to:
1 liter equals 1000 milliliters.
So, we make a rule of three:
1L ------------> 1000mL
x ---------------> 1580mL
Where the variable "x" represents the amount of liters equivalent to 1580 milliliters.
[tex]x = \frac {1580 * 1} {1000}\\x = 1.58[/tex]
Thus, 1580 milliliters equals 1.58 liters.
Anwer:
1.58 liters
Please help ASAP!!!!
The answer is B i had this problem.
Answer: OPTION B
Step-by-step explanation:
Multiply both denominators to find the Least Common Denominator:
[tex]LCD=(3y-4)(y^2)[/tex]
Now, divide each original denominator by the LCD and multiply the result by each numerator. Then:
[tex]=\frac{(6y^2+2y)(y^2)-(9y-7)(3y-4)}{(3y-4)(y^2)}[/tex]
Applying Distributive property, you get:
[tex]=\frac{6y^4+2y^3-(27y^2-36y-21y+28)}{3y^3-4y^2}\\\\=\frac{6y^4+2y^3-27y^2+36y+21y-28}{3y^3-4y^2}[/tex]
Add the like terms in the numerator:
[tex]=\frac{6y^4+2y^3-27y^2+57y-28}{3y^3-4y^2}[/tex]
What is the answer to 3 √-125/216
Answer:
2.28i
Step-by-step explanation:
u divide the -125/216
then u square root it
and multiply it times 3
YES THE I IS FOR A REASON IT MEANS IT IS IMAGINARY
2.28i I think that’s the answer but I am not sure
6.
The higher your credit score, the _____.
lower your savings interest rate
higher your car loan rate
higher risk you are to a creditor
lower your mortgage interest rate
Answer:
lower your mortgage interest rate
Step-by-step explanation:
The higher your credit score, the __lower your mortgage interest rate__.
Because the higher your credit score, the less risk you represent for a lender, so it will most likely grant you a lowest rate for your mortgage/loan.
The "lower your savings interest rate " is not the answer because savings interest rates are not related to the credit score...
"higher your car loan rate " and "higher risk you are to a creditor " are consequences of a low credit score.
what is the measure of major arc MBD
Answer:
The measure of the major arc MBD is 270°
Step-by-step explanation:
we know that
The measure of major arc MBD is equal to the sum of the measure of the arc MB plus the measure of the arc BD
BD is a diameter-----> divide the circle into two equal parts
so
arc BD=180°
arc MB is a quarter of circle
so
arc MB=90°
therefore
arc MBD=180°+90°=270°
Determine the distance between -3 and 6.
A) -9 units
B) -3 units
C) 3 units
D) 9 units
Answer:
9 units
Step-by-step explanation:
Because you start at -3 and go up so you do not add the -9 its just 9
It's 9 units because there's no such thing as -9 units!
The ratio of the lengths of an ellipse is 3:2. If it’s area is 150 cm2, what are the lengths of The major and minor semiaxes respectively?
Answer:
the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Step-by-step explanation:
Area of ellipse = π*a*b
Let major semiaxes = a and minor semiaxes = b
then a:b = 3:2
a/b = 3/2
=> a = 3/2 b
Putting in the value of formula
150 = π * (3/2)b * b
150 = 3.14 * 1.5b * b
150= 4.71 b^2
150/4.71 = b^2
=> b^2 = 31.8
b= 5.63
a = 3/2 * b
a = 1.5 * 5.63
a = 8.45
So, the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Answer:
Major: 8.5 cm
Minor: 5.6 cm
Step-by-step explanation:
Complete the square to solve the equation below check all that apply x^2+8x-2=18
x^2+8x-2=18
x^2+8x-2-18= 18-18
x^2+8x-20= 0
(x-2)(x+10)=0
x-2= 0 , x+10=0
x-2+2= 0+2, x+10-10= 0-10
x=2 , x=-10
Answers are x= 2 -B, x=-10 -A.
Answer:
Option A and B
Step-by-step explanation:
Given : Quadratic equation [tex]x^2+8x-2=18[/tex]
To find : Complete the square to solve the equation below check all that apply ?
Solution :
Re-write, [tex]x^2+8x-2=18[/tex]
[tex]x^2+8x-20=0[/tex]
Applying quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1 , b=8, c=-20
[tex]x=\frac{-8\pm\sqrt{8^2-4(1)(-20)}}{2(1)}[/tex]
[tex]x=\frac{-8\pm\sqrt{64+80}}{2}[/tex]
[tex]x=\frac{-8\pm\sqrt{144}}{2}[/tex]
[tex]x=\frac{-8\pm12}{2}[/tex]
[tex]x=-4\pm6[/tex]
[tex]x=-4+6,-4-6[/tex]
[tex]x=2,-10[/tex]
The solution of the equation is x=2,-10.
Therefore, Option A,B satisfy the equation.
8. Kristen borrowed $700 at a
simple interest rate of 15% for 3
years. How much interest will
Kristen pay?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(700)(0.15)(3)\implies I=315[/tex]
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. The Tigerd family orders a large pizza topped with pepperoni, mushrooms, olives, and sausage. How much did their pizza cost?
Answer:
$18.99
Step-by-step explanation:
Step 1: Take the per topping amount ($1.25) and multiply it by the amount of toppings (4). $1.25x4=$5
Step 2: Add your toppings total ($5) to the base pizza cost ($13.99). $13.99+$5=$18.99
Answer:
18.99
work:
13.99 + (1.25 x 4 )
13.99 + 5
18.99
trust me, 18.99 + (1.25 x 4) will work and the work showing also
Lydia wanted to flip a coin and roll a die at the same time, but she also wondered what the probability of the coin landing on heads and the die landing on a 5 would be. She did a little bit of thinking and came up with 1/4 as the probability.
In complete sentences, determine if Lydia is correct or incorrect and explain using what you know about compound probability of independent events.
Answer:
incorrect
Step-by-step explanation:
this is because it would be 1/2 and 1/6. you would have to multiply the bases for a probability of 1/12
Annie had 7 apples, she sold 5 of them, and bought 3 more apples. Annie gave 2 apples to her friends, and then lucy gave her 9 apples, annie ate 6 apples, and found 89 more apples. How many apples does annie have now?
Answer:
Annie has 95 apples now
Answer:
Annie has 95 Apples
Step-by-step explanation:
7 Apples - 5 Apples = 2
2 + 3 more apples = 5 Apples
5 Apples - 2 Apples = 3 Apples
3 Apples + 9 more apples = 12 Apples
12 - 6 = 6 Apples
6 Apples + 89 more apples = 95 Apples
12 ÷2x3-(7-5)=?
Please help me solve this equation.
Answer:
16
Step-by-step explanation:
18-(7-5)
18-2=16
Answer:
16
Step-by-step explanation:
12 ÷ 2 × 3 - (7 - 5)
= 12 ÷ 2 × 3 - (2)
= 6 × 3 - 2
= 18 - 2
= 16
Mr. Grocer has 421 dozen eggs valued at $0.59 per dozen. How much are the eggs worth altogether?
248.39
713.56
420.41
421.59
Answer:
248.39
Step-by-step explanation:
421 × .59 =248.39
Please help me it urgent find the total area.
I'll split this figure up in three sections, 65*60, 70*190, and 95*140.
95*140=13300
70*190=13400
65*60= 3900
Add the three areas of the three figures I have split the original figure into and you get 30600 ft²
Which phrase best describes the translation from the graph y = 2x2 to the graph of y = 2x2 + 5?
ANSWER
5 units up
EXPLANATION
The given function is
[tex]y = 2 {x}^{2} [/tex]
The new graph is
[tex]y = 2 {x}^{2} + 5[/tex]
The new function is obtained by adding 5 to the original function.
This will shift the graph up by 5 units.
The translation is a vertical shift up by 5 units.
Answer:
The translation is 5 units up
Step-by-step explanation:
+5 on the outside means up by 5
85 kilometers is equal to how many meters
Answer:
85 kilometers is equal to 85 000 meters
Step-by-step explanation:
1 kilometer is equivalent to 1000 meters. Then to convert from kilometers to meters use the following conversion factor
[tex]x\ kilometers * \frac{1000\ meter}{1\ kilometers }[/tex]
In this case [tex]x=85[/tex]
Then
[tex]85\ km* \frac{1000\ m}{1\ km} =85,000\ m[/tex]
Finally 85 kilometers = 85,000 meters
Answer:
85km = 85,000mStep-by-step explanation:
1km - one kilometer
kilo - 1,000 times more
1km = 1,000m
therefore
85km =85 × 1,000m = 85,000m
Factor 27a^3 b^9+8c^18
Answer:
(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12)
Step-by-step explanation:
Given:
Polynomial 27a^3 b^9+8c^18
Factoring the given polynomial
27a^3b^9 can be written as
=3^3.a^3.b^3^3
=(3ab^3)^3
Also 8c^18 can be written as
=2^3.c^6^3
=(2c^6)^3
Hence Polynomial 27a^3 b^9+8c^18 can be written as
=(3ab^3)^3+(2c^6)^3
Applying sum of cubes formula i.e. a^3 + b^3=(a+b)(a^2 – ab + b^2)
=(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12) !
Find the output, b, when the input, a, is 6.
B = -1 - 7a
B=
output B= -1-7*(6)
so -7*6=-42
-1-42= -43
The value of the linear equation B = - 1 - 7a at a = 6 will be negative 43.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The equation is given below.
B = - 1 - 7a
The value of the equation at a = 6. Then we have
B = - 1 - 7 × 6
B = - 1 - 42
B = - 43
The value of the linear equation B = - 1 - 7a at a = 6 will be negative 43.
More about the solution of the equation link is given below.
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Can someone help with this plz?
Answer:
Hey No worries. Its very easy.
Step-by-step explanation:
Look,
Volume= 84 in.cube
Length=6 in.
Breadth=2 in.
therefore, Height= Volume/(Length*Breadth)
=84/(6*2)
=84/12
=7
Answer:
h = 7 in
Step-by-step explanation:
The volume (V) of a cuboid is calculated using the formula
V = lbh ( l is length, b is breadth and h is height )
Given V = 84 in³, then
lbh = 84 ← substitute l = 6 and b = 2
6 × 2 × h = 84
12h = 84 ( divide both sides by 12 )
h = 7
Help me find the domain of this function please
Answer:
Domain: {-12, 0, 24, 60}
Step-by-step explanation:
Function:
f(x) = [tex]\frac{x}{12}[/tex]
Range: { -1, 0, 2, 5}
For range = -1,
Domain: -1 = [tex]\frac{x}{12}[/tex] ⇒ x = -12
For range = 0,
Domain: 0 = [tex]\frac{x}{12}[/tex] ⇒ x = 0
For range = 2,
Domain: 2 = [tex]\frac{x}{12}[/tex] ⇒ x = 24
For range = 5,
Domain: 5 = [tex]\frac{x}{12}[/tex] ⇒ x = 60
Domain: {-12, 0, 24, 60}
c/3 = 30/5 what steps do I take to see what c is?
For this case we must find the value of "c" of the following expression:
[tex]\frac {c} {3} = \frac {30} {5}[/tex]
We solve the right side of the equation:
[tex]\frac {30} {5} = 6[/tex]
Rewriting:
[tex]\frac {c} {3} = 6[/tex]
We multiply both sides of the equation by "3":
[tex]c = 6 * 3\\c = 18[/tex]
Answer:
[tex]c = 18[/tex]
Which of the following is a composite number? A. 23 B. 11 C. 25 D. 19
The composite number among options A. 23, B. 11, C. 25, D. 19 is C. 25. Composite numbers have more than two factors, and 25 has factors 1, 5, and 25.
Explanation:The question is asking to identify which of the given options is a composite number. A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In simpler terms, composite numbers have more than two factors.
Now let's evaluate the given numbers:
23 and 19 are prime numbers because they have only two factors which are 1 and the number itself.11 is also a prime number with only two factors which are 1 and 11.25 has factors 1, 5, and 25. Hence, it is a composite number.Therefore, 25 is the composite number among the given options.
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The composite number among the options is C. 25.
Explanation:A composite number is a positive integer greater than 1 that has more than two distinct positive divisors. In other words, it is not a prime number. Examples include 4 (divisible by 1, 2, and 4) and 9 (divisible by 1, 3, and 9).
Thus, a composite number is a positive integer that has more than two divisors. To determine whether a number is composite or not, we check if it is divisible by any number other than 1 and itself. Among the given options, 25 is a composite number because it can be divided evenly by 5 and 1, in addition to 25 and itself.
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Write the equation of the line that passes through the points (7, –4) and (–1, 3), first in point-slope form, and then in slope-intercept form.
The slope of the line is .
When the point (7, –4) is used, the point-slope form of the line is .
The slope-intercept form of the line is .
Answer:
The slope of the line is -7/8
When the point (7, –4) is used, the point-slope form of the line is
y+4=(-7/8)(x-7)
The slope-intercept form of the line is y=(-7/8)x+(17/8)
Step-by-step explanation:
Answer:
y+4=(-7/8)(x-7)
Step-by-step explanation:
which inequality is equalivalent to |x-4|<9
Answer:
-5 < x < 13Step-by-step explanation:
[tex]|x-4|<9\iff x-4<9\ \wedge\ x-4>-9\qquad\text{add 4 to both sides}\\\\x<13\ \wedge\ x>-5\to-5<x<13[/tex]
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores.
88%, 73%, 97%, 76%, 90%, 80%
Which measure of center would best represent Ari’s grade?
Answer:
Mean because it is the average of all of them combined = best representation of all grades.
84% & Mean
Step-by-step explanation:
88 + 73 + 97 + 76 + 90 + 80 = 504
**divide by how many grades there are** (6 of them)
504 / 6 = 84
Meaning the best center representation would be 84%
Answer: The Mean
The mean is when you add up all of those grades and divide by the amount of exams.
HELP! 18 points for the two questions!! urgent will mark brainliest
Answer:
1- none of the choices are correct.
2-none of the answer choices are correct.
Step-by-step explanation:
1- there is no k therefore none are correct because they all offer a solution for k
2- yes the parabola opens upward but none are right in the right mix for the other two. the vertex is at (0,-5) and the axis of symmetry is x = 0 (not only because I calculated it and the graph showed it but because (x,y) And the x spot is a 0)
any time you just see a plain x^2 or really anything like that in the same vanilla sense wether the exponent is changed or there is a coefficient and all it has is a plus or minus whatever it will just be along the y axis where the plus or minus number was. (can't remember any vanilla advice for parabolas sorry)
Answer:
1. a=5,h=0,k=0
2. None of the choices are correct
Step-by-step explanation:
1. The function given is:[tex]f(x)=5x^2[/tex]
We can rewrite this in vertex form as: [tex]f(x)=5(x-0)^2+0[/tex].
Comparing this to [tex]f(x)=a(x-h)^2+k[/tex], we have a=5,h=0 and k=0.
The first choice is correct
2. The function given is: [tex]f(x)=x^2-5[/tex]
This can be rewritten in the vertex form as:
[tex]f(x)=a(x-0)^2-5[/tex]
Comparing this to [tex]f(x)=a(x-h)^2+k[/tex], we have a=1,h=0 and k=-5.
Since 'a' is positive, the parabola opens upwards, and has its vertex at (h,k)=(0,-5), and line of symmetry at x=0.
Based on this, the correct choice is none of the choices are correct
find the missing angle measure in each figure
Answer:
x = 100°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 7, hence
sum = 180° × 5 = 900°
Sum the given interior angles and equate to 900
x + 155 + 116 + 135 + 135 + 116 + 143 = 900
x + 800 = 900 ( subtract 800 from both sides )
x = 100°
A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of exam scores are between 400 and 600?
__% of exam scores are between 400 and 600.
Answer:
68% of exam scores lie within one std. dev. of the mean
Step-by-step explanation:
Because the standard deviation is 100, one standard deviation above the mean comes out to 600. Likewise, one std. dev. below the mean comes out to 400. By the Empirical Rule, 68% of exam scores lie within one std. dev. of the mean.
Answer:
[tex]P(400<x<600) = 68.3\%[/tex]
Step-by-step explanation:
We know that the average [tex]\mu[/tex] is:
[tex]\mu=500[/tex]
The standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=100[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
We seek to find
P(400<x<600)
This is:
[tex]P(400<x<600)=P(\frac{400-500}{100}<\frac{x-\mu}{\sigma}<\frac{600-500}{100})\\\\P(400<x<600)=P(-1<Z<1)[/tex]
Looking for the value of z in a normal table we have to:
[tex]P(Z>1) =0.1587\\\\P(Z>-1) = 0.8413[/tex]
So
[tex]P(-1<Z<1)=P(Z>-1) - P(Z>1) =0.8413-0.1587=0.6826\\\\P(400<x<600) = 68.3\%[/tex]