Answer:
all of your answers are correct
1.) 64
2.) x= -5+4i and x= -5-4i
3.) (4x+3iy)(4x-3iy)
Answer:
1.When we are completing squares, we need to divide by 2 the linear term and then find its square power, that's the term we need to add on both sides of the equality, as follows
[tex](\frac{16}{2})^{2} =(8)^{2}=64[/tex]
Basically, we need to add the number 64 both sides
[tex]x^{2} +16x+64=18+64[/tex]
2.The given equation is
[tex]x^{2} +10x+41=0[/tex]
We need to apply the quadratic formula to solve this equation
[tex]x_{1,2} =\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Where [tex]a=1[/tex], [tex]b=10[/tex] and [tex]c=41[/tex]. Replacing these values, we have
[tex]x_{1,2} =\frac{-10(+-)\sqrt{10^{2}-4(1)(41) } }{2(1)}\\x_{1,2} =\frac{-10(+-)\sqrt{100-164 } }{2}=\frac{-10(+-)\sqrt{-64} }{2}[/tex]
There we need to use complex number, to transform the subradical number in a positive number
[tex]x_{1,2}=\frac{-10(+-)\sqrt{64}i }{2}=\frac{-10(+-)8i}{2}\\ x_{1,2}=-5(+-)4i[/tex]
Therefore, the complex solutions are
[tex]x_{1}=-5+4i\\ x_{1}=-5-4i[/tex]
3.The given expression is
[tex]16x^{2} +9y^{2}[/tex]
To solve this expression, remember that [tex]i=\sqrt{-1}[/tex]
First, we expresse both squares uniformly,
[tex]16x^{2} +9y^{2}=(4x)^{2}+(3y)^{2}[/tex]
But, we know that [tex]-(-1)=1[/tex], so
[tex](4x)^{2}+(3y)^{2}=(4x)^{2}-(-1)(3y)^{2}[/tex]
Then,
[tex](4x)^{2}-(-1)(3y)^{2}=(4x)^{2}-(3y)^{2}i^{2}[/tex], because [tex]i^{2}=-1[/tex]
Therefore, the expression with complex numbers is
[tex](4x)^{2}-(3iy)^{2}\\\therefore (4x+3iy)(4x-3iy)[/tex]
Sam is building a model of an antique car the scale of his model to the actual car is 1:10 his model is 16 1/2 inches long. How long is the actual car
16.5(10)=165
The length of the actual car is 165in.
Find the value of x to the nearest tenth.I will mark the brainlest
Answer:
1.6 = x
Step-by-step explanation:
For right angles, tan x = opposite/adjacent
tan 37 = x / 2.1
Multiply 2.1 on each side.
2.1 tan 37 = x
1.58246 =x
Rounding to the nearest tenth
Victor needs 30 feet of rope. The rope he wants to buy is sold by the yard. He knows that there are 3 feet in 1 yard. How many yards should he buy
NeeD HELP ASAP ! Please. the function f(x)=x^2. The graph of g(x) is f(x) translated to the right 3units and down 3 units what is the function rule for g(x) ? Please show me step by step
Answer:
g(x) = (x-3) ^2 -3
Step-by-step explanation:
f(x) = x^2
To shift down 3 units, subtract 3 ( When we move up, we add)
h(x) = x^2 -3
To shift to the right 3 units, replace x with (x-3). I know it seems backwards, but right is minus and left is plus.
g(x) = (x-3) ^2 -3
Robert wanted to know if the type of phone you used gave you better or worse service. Define the dependent and independent variables.
Answer:
Independent Variable - Type of Phone
Dependent Variable -Type of Service
Step-by-step explanation:
2) On a trip to the movies a family spent $35 on tickets, and another $25 on popcorn. They also spent $10 on drinks. The oldest son spent some money on candy. Altogether the family spent $76. How much did the oldest son spend on candy?
Find the ordered pair (s, t) that satisfies the system
s/2 - 3t = -1
3t - 2s = 3
[tex]\left\{\begin{array}{ccc}\dfrac{s}{2}-3t=-1&\text{multiply both sides by 4}\\3t-2s=3\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2s-12t=-4\\3t-2s=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad -9t=-1\qquad\text{divide both sides by (-9)}\\.\qqud\qquad\boxed{t=\dfrac{1}{9}}\\\\\text{Put the value of t to the second equation}\\\\3\left(\dfrac{1}{9}\right)-2s=3\\\\\dfrac{1}{3}-2s=3\qquad\text{subtract}\ \dfrac{1}{3}\ \text{from both sides}[/tex]
[tex]-2s=2\dfrac{2}{3}\qquad\text{divide both sides by (-2)}\\\\s=\dfrac{8}{3}\cdot\left(-\dfrac{1}{2}\right)\\\\\boxed{s=-\dfrac{4}{3}}\\\\Answer:\ \boxed{\left(-\dfrac{4}{3},\ \dfrac{1}{9}\right)}[/tex]
By simplifying and rearranging the given system of equations, we find that the ordered pair (s, t) that satisfies the system is (2, 1 + 2/3).
Explanation:The system of equations given in the question is:
s/2 - 3t = -1
3t - 2s = 3.
We can begin solving this system by first multiplying the first equation by 2 to eliminate the fraction, giving us:
s - 6t = -2.
Next, we rearrange the second equation to be in terms of 's':
2s = 3t + 3.
We then substitute this into the first equation and solve for 't':
(3t + 3) - 6t = -2,
simplifying to:
-3t + 3 = -2,
leading us to t = 1 + 2/3.
Substituting 't' into the second equation to find 's', we get:
2s = 3(1 + 2/3) + 3, which simplifies to s = 2. Therefore the ordered pair (s,t) that satisfies the system of equations is (2, 1 + 2/3).
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Is the simplified form of 2√3 − 2√3 rational?
Yes
No
Answer:
Yes
Step-by-step explanation:
2√3 − 2√3 is equal to 0. So what we are trying to find out is if 0 is a rational number. 0 IS a ratinol number as it can be expressed as a fraction of integers.
Whose orange juice mixture tastes stronger? Explain or show your reasoning.
Clare mixes 2 1/2 cups of water with 1/3 cup of orange juice concentrate.
Han mxes 1 2/3 cups of water with 1/4 cup of orange juice
Answer:Han's mixture tastes stronger
Step-by-step explanation: Han's mixture tastes stronger, because...
Han's uses 6 2/3 cups of water for every 1 cup of orange juice concentrate.
Clare uses 71/2 cups of water for every 1 cup of orange juice concentrate.
Answer:
Han's juice has 15% concentration which is larger and hence, his juice will be stronger.
Step-by-step explanation:
It is required to find that which juice is stronger. So, we need to find the juice with maximum fraction or percentage of juice out of both the cases.
In first case, Clare mixes [tex]2\dfrac{1}{2}=\dfrac{5}{2}[/tex] cups of water with [tex]\dfrac {1}{3}[/tex] cup of orange juice. So, the concentration of the juice will be,
[tex]\dfrac{1/3}{5/2}=\dfrac{2}{15}=13.33\%[/tex]
In the second case, Han mixes [tex]1\dfrac{2}{3}[/tex] cups of water with [tex]\dfrac{1}{4}[/tex] cup of orange juice.
So, the concentration of the juice will be,
[tex]\dfrac{1/4}{5/3}=\dfrac{3}{20}=15\%[/tex]
Therefore, out of the two cases, Han's juice has 15% concentration which is larger and hence, his juice will be stronger.
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The sum of two numbers is 46 and the difference is 10 . What are the numbers?
Answer: 28 and 18
Step-by-step explanation:
I used the guess and test strategy to find that:
28 - 10 = 18
28 + 18 = 46
will mark brainliest !!
how do you calculate acceleration
Answer:
You use F = m x a to solve for acceleration. You can change this formula around to solve for acceleration by dividing both sides by the mass, so: a = F ÷ m. To find the acceleration, simply divide the force by the mass of the object being accelerated.
HOPE IT HELPS
F= Force
A = Acceleration
M = Mass
Answer:
a=v/t
Step-by-step explanation:
to find acceleration divide change in velocity and change in time!
Hope this helps!!
Have a great day!
please help me as soon as u can!!
Urgent
thankssss
Q2 Answer: Experimental = 60%, difference = 10%
Step-by-step explanation:
The prime numbers between 1 and 8 are: 2, 3, 5, and 7.
Theoretical: [tex]\dfrac{4(prime)}{8(total)} = 50\%[/tex]
Experimental: [tex]\dfrac{12(prime)}{20(total)} = 60\%[/tex]
Experimental - Theoretical
= 60% - 50%
= 10%
Problem 1
To find the sample mean, we simply add up all the 40 items and then divide by 40
I will add up the values row by row, and then add up the subtotals to get the grand total
row1: 39+31+38+40+29 = 177
row2: 32+33+39+35+32 = 171
row3: 32+27+30+31+27 = 147
row4: 30+29+34+36+25 = 154
row5: 30+32+38+35+40 = 175
row6: 29+32+31+26+26 = 144
row7: 32+26+30+40+32 = 160
row8: 39+37+25+29+34 = 164
Add up the subtotals: 177+171+147+154+175+144+160+164 = 1292
Divide this over 40: 1292/40 = 32.2
So the sample mean is therefore 32.2
-----------------------
To find the proportion of defective items, we count the number of times a value less than 26 shows up. That happens exactly two times. The first in row 4 (at the end of this row) is where a 25 shows up. Another copy of 25 shows up in row 8 (bottom row). There are no other values that are less than 26.
Divide this count (2) over the total sample size (40) and we get 2/40 = 1/20 = 0.05
-----------------------
In summary, 32.2 will go in the first box while 0.05 will go in the second box.
========================================
Problem 2
There are 4 values we want (2,3,5,7) out of 8 total (1,2,3,4,5,6,7,8) so 4/8 = 0.50 = 50% is the theoretical probability
This is the list of values given to us (I broke it up to help make the numbers more readable)
3, 4, 5, 2, 7
1, 3, 7, 2, 6
2, 1, 7, 3, 6
1, 8, 3, 5, 6
Of that list, the primes {3, 5, 2, 7, 3, 7, 2, 2, 7, 3, 3, 5} show up. There are 12 primes in this list out of 20. So the experimental probability is 12/20 = 3/5 = 0.60 = 60%
Therefore, the answer that goes in the "experimental probability" box is 60. The answer that goes in the second box is not 50%. I think your teacher is aiming for "10" to go in the second box because 60% is 10 percentage points higher than 50% (which was the theoretical probability found earlier)
-----------------------
In summary, 60 will go in the first box while 10 will go in the second box.
Please answer this question! 30 points and brainliest!
Answer:
c x >=3
Step-by-step explanation:
9-2x <= 3
Subtract 9 from each side
9-9-2x <=3-9
-2x <-6
Divide by -2. Remember to flip the inequality when multiplying or dividing by a negative number.
-2x/-2 >= -6/-2
x >=3
Answer: i think it would be letter c plz mark brainliest and add as friend
You can find the rise by _ the Y-coordinate of the left point from the y-coordinate of the right point
Answer:
Subtracting
Step-by-step explanation:
We know that the slope of a line is given by the rise over run. where rise is vertical difference between two points and run is the horizontal distance between the points.
[tex]\text{if }(x_1,y_1) \text{ and }(x_2,y_2)\text{ are two points on a line, then the}\\\text{slope of the line is given by}\\\\\text{Slope, }m=\frac{y_2-y_1}{x_2-x_1}\\\\\text{since slope}=\frac{\text{Rise}}{\text{Run}}, \text{ so Rise}=y_2-y_1\\\\\text{so we can find the rise by subtracting the Y-coordinate of the left point }\\\text{from the y-coordinate of the right point}.[/tex]
A bar of gold has a volume of 722 cubic centimeters and weighs 13.949 kilograms. What's its density in grams per cubic centimeter?
Answer:
The density of the bar of gold is 19.32 grams per cubic centimeter .
Step-by-step explanation:
Formula
[tex]Density = \frac{Mass}{Volume}[/tex]
As given
A bar of gold has a volume of 722 cubic centimeters and weighs 13.949 kilograms.
As 1 kilogram = 1000 gram
Than convert 13.949 kilograms into grams.
13.949 kilograms = 13.949 × 1000 grams
= 13949 grams
Mass = 13949 grams
Volume = 722 cubic centimeter
As put in the formula
[tex]Density = \frac{13949}{722}[/tex]
Density = 19.32 grams per cubic centimeter (Approx)
Therefore the density of the bar of gold is 19.32 grams per cubic centimeter .
In Sakura's garden, for every 55 red flowers, there are 1010 yellow flowers. There are a total of 7575 yellow and red flowers in her garden. How many red flowers are in Sakura's garden?
Answer:
The answer is 25
Step-by-step explanation:
Therefore, there are 25 red flowers in Sakura’s garden1.
We know that for every 55 red flowers, there are 1010 yellow flowers.
The total number of flowers in the garden is 7575 (which includes both red and yellow flowers).
Let’s use the variable (x) to represent the number of red flowers in the garden. We can set up the following ratio:
[tex][ \frac{{\text{{Red flowers}}}}{{\text{{Total flowers}}}} = \frac{{55}}{{55 + 1010}} ][/tex]
Solving for (x):
[tex][ \frac{{\text{{Red flowers}}}}{{7575}} = \frac{{55}}{{55 + 1010}} ][/tex]
Cross-multiplying:
[tex][ 55 \cdot 7575 = 55x + 1010x ][/tex]
Simplifying:
[tex][ 7575 = 55x + 1010x ][/tex]
Combining like terms:
[tex][ 7575 = 1065x ][/tex]
Solving for (x):
[tex][ x = \frac{{7575}}{{1065}} = 25 ][/tex]
a positive number is 5 times less than another positive number. Six times the lesser number plus 3 times the greater is 3. Find the two positive numbers
Answer:
One number is [tex]\frac{5}{7}[/tex] and the other number is [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
Let x be the smaller number and y be the bigger number.
x = x
y = 5x
6x + 3y = 3
6x + (3 * 5x) = 3
6x + 15x = 3
(÷3)
2x + 5x = 1
7x = 1
x = [tex]\frac{1}{7}[/tex]
6x + 3y = 3
6([tex]\frac{1}{7}[/tex]) + 3y = 3
[tex]\frac{6}{7}[/tex] + 3y = 3
3y = 3 - [tex]\frac{6}{7}[/tex]
3y = [tex]\frac{15}{7}[/tex]
Divide both sides by 3 to get 1y:
y = [tex]\frac{5}{7}[/tex]
So one number is [tex]\frac{5}{7}[/tex] and the other number is [tex]\frac{1}{7}[/tex]
Using the linear combination method, what is the solution to the system of linear equations 7x-2y=-20 and 9x+4y=-6 ?
Answer:
The answer would be well, B.(-2,3)
The given system of equations are solved to obtain x = -2 and y = 3.
What are the types of a system of equations?The given system of equation can either have a unique solution, more than one solutions or no solution.
On this basis they are divided into two parts consistent and inconsistent.
A consistent system has one or more solutions while for an inconsistent system there are no solutions.
The equations are given as,
7x - 2y = -20 (1)
9x + 4y = -6 (2)
Multiply equation (1) by 2 and then add to (2) to get,
2(7x - 2y) + 9x + 4y = -20 × 2 + (-6)
⇒ 23x = -46
⇒ x = -2
Then, substitute x = -2 in equation (1) to get,
7 × -2 - 2y = -20
⇒ y = 3
Hence, the solution of the given system of equations is given as x = -2 and y = 3.
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The ___________ is the center of gravity in a triangle.
A) centroid
B) circumcenter
C) incenter
D) orthocenter
Answer:
A) centroid
Step-by-step explanation:
I just looked it up.
Answer:
A. Centroid
Step-by-step explanation:
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. The centroid is also called the center of gravity of the triangle.
What is the resulting equation when the expression for y in the second equation is substituted into the first equation?
3x + y = 1
y = 6 - 4x
A.-x + 6 = 1
B.x + 6 = 1
C.7x + 6 = 1
Answer: 3x + 6 -4x = 1
Simplify to -x + 6 = 1 because 3x - 4x = -1x
find the area of a rectangle whose vertices are (2,2),(-3,2),(2,8), and (-3,8)
Answer:
Area of rectangle = 30 units
Step-by-step explanation:
vertices are (2,2),(-3,2),(2,8), and (-3,8)
Let find the distance between (2,2) and (2,8). because they have same x values. that would be our width
distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}[/tex]
D = [tex]\sqrt{(2-2)^2 + (8-2)^2}=\sqrt(6^2) = 6[/tex]
Width = 6
Now we find distance between (2,2) and (-3,2) because they have same y values, that would be our length
distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}[/tex]
D = [tex]\sqrt{(-3-2)^2 + (2-2)^2}=\sqrt(-5^2) = \sqrt(25)= 5[/tex]
length = 5
Area of rectangle = length * width = 5*6 = 30
A length of rope is stretch between the top edge of the building at stake in the ground the head of the state is at ground level the rope also touches a tree that is growing halfway between the state and the building if the tree is 38 feet tall how tall is the building
Because the tree is the halfway point, the building would be twice as tall:
The building is 38 x 2 = 76 feet tall.
Answer:
76 feet
Step-by-step explanation:
based on the looooooong txt, the building n tree form two similar right-angled triangles w the rope as the hypothesis.
tree is halfway between stake and bldg so stake-to-bldg = 2 x stake-to-tree
as the triangles are similar, their sides are in the same ratio
bldg height = 2 x tree height
= 2 x 38
= 76 feet tall
The charge for ice skating is $3 for the skate rental and and 2 per hour to skate how much will you pay if you skate
Brady rode his bike 70 miles in 4 hours he rode at an average speed of 17 mph for t hours and at an averege rate of speed of 22 mph for the rest on the time how long did brady ride at the lower speed
i think it will be 5 minutes
HELP CHECK THIS
The work of a student to solve a set of equations is shown:
Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z
Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3
In which step did the student first make an error?
Step1
Step 2
Step 3 <<<<<
Step 4
HELP!!!!! 50 POINTS!!
Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Basically here all you want to do it substitute the values x=1 and x=2 for the given function. Use your slope formula [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex].
Do same for x=3 and x=4
You next divide plug in values in to this expression:
[tex]\frac{Slope of B}{Slope of A}[/tex]
Christian reads 14 book every 23 week. How many books does Christian read per week?
hurryy plesssss help me
Answer:
0.609 / week ( to nearest thousandth)
or you can state it as 60.9% of a book per week
Step-by-step explanation:
That would be 14/23 = 0.609 / week
Which of the following is not a polynomial? Question is in the picture.
Answer:
4-x
Step-by-step explanation:
u can tell cause it doesn't have the exponent on the top and all that jazz
Which statement is true ? Help plzzzz
Answer:
Correct choice is B
Step-by-step explanation:
The quadratic function g(x) has equation [tex]g(x)=ax^2+bx+c.[/tex] Find values of a, b and c:
[tex]g(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2.[/tex]
[tex]g(2)=3=a\cdot 2^2+b\cdot 2++2\Rightarrow 4a+2b=1.[/tex]
[tex]g(4)=2=a\cdot 4^2+b\cdot 4+2\Rightarrow 16a+4b=0.[/tex]
From the last equation [tex]b=-4a[/tex] and [tex]4a-8a=1,\\ \\a=-\dfrac{1}{4},\\ \\b=1.[/tex]
The equation of the quadratic function g(x) is
[tex]g(x)=-\dfrac{1}{4}x^2+x+2.[/tex] This quadratic function determines the parabola with vertex at point (3,2). Thus,
1. The maximal value of f(x) is 4 at x=2.
2. The maximal value of g(x) is 3 at x=2.
Thus, the maximal value of f(x) is greater than the maximal value of g(x). So option B is correct.
At the grocery store, Vanessa bought 1.02 pounds of ground beef, 1.6 pounds of tomatoes, and 1.2 pounds of chicken. How much did these three items weigh altogether?
Answer:
3.82 pounds.
Step-by-step explanation:
We have been given that at the grocery store, Vanessa bought 1.02 pounds of ground beef, 1.6 pounds of tomatoes, and 1.2 pounds of chicken.
To find the total weight of three items, let us add 1.02, 1.6 and 1.2.
[tex]\text{The total weight of three items}=1.02+1.6+1.2[/tex]
[tex]\text{The total weight of three items}=3.82[/tex]
Therefore, three items weigh 3.82 pounds altogether.
Final answer:
Vanessa bought a total of 2.82 pounds of food, calculated by adding the weight of the ground beef, tomatoes, and chicken she purchased.
Explanation:
To calculate the total weight of the ground beef, tomatoes, and chicken Vanessa bought, simply add up their weights:
Ground beef: 1.02 pounds
Tomatoes: 1.6 pounds
Chicken: 1.2 pounds
To find the sum, you can add these values together:
1.02 + 1.6 + 1.2 = 2.82 pounds
So, Vanessa bought a total of 2.82 pounds of food.