Answer: {-7, 2}
Step-by-step explanation: This type of equation is called a polynomial equation and in order to solve for x, we would first factor the left side.
Notice that the left side of the equation is a trinomial in a special
form that can be factored as he product of two binomials.
As our first term for each binomial, we have the factors of x², x · x
and as the second term, we have the factors of -14 that add to 5.
In this case, the factors are +7 and -2.
So we have (x + 7)(x - 2) = 0.
If (x + 7)(x - 2) = 0, that means that either x + 7 = 0 or x - 2 = 0.
Solving for x in each equation, we have x = -7 or x = 2.
We can write our answer as the solution set {-7, 2}.
The solution of quadratic equation is,
⇒ x = - 7, 2
We have to given that,
An equation is,
⇒ x² + 5x - 14 = 0
We can factorized the above quadratic equation as,
⇒ x² + 5x - 14 = 0
⇒ x² + (7 - 2)x - 14 = 0
⇒ x² + 7x - 2x - 14 = 0
⇒ x (x + 7) - 2 (x + 7) = 0
⇒ (x + 7) (x - 2) = 0
This gives,
x + 7 = 0
x = - 7
x - 2 = 0
x = 2
Therefore, The solution of quadratic equation is,
⇒ x = - 7, 2
Learn more about the quadratic equation visit:
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SOMEONE PLS HELP PRECALCULUS
Sine is negative in quadrants 3 and 4, when y < 0.
Tangent is negative for quadrants 2 and 4, when y/x < 0. Basically when x and y differ in sign (one is positive, the other is negative)
The common quadrant mentioned is quadrant 4.
Quadrant 4 has angles that are between 270 degrees and 360 degrees
So we have [tex]270^{\circ} < \theta < 360^{\circ}[/tex]
Answer: Choice DDetermine the constant of proportionality in the situation below. Six bags of sunflower seeds cost $7.20
Answer:
1.20 for each bag of sunflower seeds
Step-by-step explanation:
Answer: $1.20 per bag
Step-by-step explanation:
[tex]\dfrac{\$7.20}{6\ bags}\div \dfrac{6}{6}\quad = \quad \dfrac{\$1.20}{1\ bag}[/tex]
Question: Using substitution, identify the ordered pair that is not an element of the solution set of the system of equations. 3x − y = 2 6x − 2y = 4 Answers: (1, 1) (−2, −4) (0, −2) (2, 4)
Answer:
(-2, -4)
Step-by-step explanation:
3(-2) - -4 = -2, so it doesn't work.
both equations are the same line
8 elementary classes will be chosen to participate in a school lunch survey. There are 23 elementary classes in the school. In how many ways can the classes be chosen?
Answer:
490,314
Step-by-step explanation:
This is a combinations problem. The formula is n!/(n-r)!xr!
This is 23!/(23-8)!x8!=
23!/15!x8!=
19,769,460,480/40,320=
490,314
Using the combination formula, it is found that the classes can be chosen in 490,314 ways.
The order in which the classes are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 8 classes are chosen from a set of 23, hence:
[tex]C_{23,8} = \frac{23!}{8!(15)!} = 490314[/tex]
The classes can be chosen in 490,314 ways.
More can be learned about the combination formula at https://brainly.com/question/25821700
Mrs. Fox bought a bag of cookies for her math club students. If she gives each student 5 cookies, she will have 14 cookies left over. If she has 4 additional cookies, each student could receive 7 cookies and no cookies left over. How many students are in Mrs. Fox’s math club?
Answer:
9
Step-by-step explanation:
7x=5x+14+4
7x=5x+18
2x=18
x=9
Jerry solved the system of equations. x minus 3 y = 1. 7 x + 2 y = 7. As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement? The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution. The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7. The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2. The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
Answer:
A. The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
Given
[tex]Equation\ 1: x - 3y = 1[/tex]
[tex]Equation\ 2: 7x + 2y = 7[/tex]
Required
Efficient way of solving the equations
The efficient way of solving this problem is by solving for x in the first equation because it has a coefficient of 1;
The evidence is shown as follows;
Make x the subject of formula in equation 1
[tex]x = 1 + 3y[/tex]
Substitute 1 + 3y for x in equation 2
[tex]7x + 2y = 7[/tex]
[tex]7(1 + 3y) + 2y = 7[/tex]
Open bracket
[tex]7 + 21y + 2y = 7[/tex]
[tex]7 + 23y =7[/tex]
Make y the subject of formula
[tex]23y = 7 - 7[/tex]
[tex]23y = 0[/tex]
Divide both sides by 23
[tex]\frac{23y}{23} = \frac{0}{23}[/tex]
[tex]y = 0[/tex]
Recall that x = 1 + 3y
Substitute 0 for y in the above expression
[tex]x = 1 + 3(0)[/tex]
[tex]x = 1 + 0[/tex]
[tex]x = 1[/tex]
Solving for y in the second equation will take more steps
Answer:
A: The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
which sentence is represented by this algebraic equation "X/2-3=15"
Answer:
A
Step-by-step explanation:
The correct answer is A.
"3 less than" represents -3
"half of x" represents x/2
"is 15" represents =15
Solve 6x^2 +5x - 4 = 0 by factoring. Enter each step. please help me.
Answer:
x = 0.36
Step-by-step explanation:
6x^2 +5x - 4 = 0
6x+5x-4 = 0÷2
11x = 0+4
x = 4÷11
Therefore, x = 0.36
PLEASE HELP! 20 POINTS
Answer:
question 1: 5/9 question 2: 9/5
Step-by-step explanation:
10/18 can be simplified to 5/9
18/10 can be simplified to 9/5
Mikel has a chance to win a trip on a TV game show. All he has to do is win the "Shopping Game". In this game, Mikel is shown six grocery store items without being shown the prices. He must buy multiples of items until he has a total between $20 and $21 inclusive. If he doesn’t reach $20 with his first item, he continues buying items and adding to his total, until he either wins by getting an amount between $20 and $21, or he loses by going over $21 or by buying all items and being less than $20. First, Mikel buys six bottles of shampoo.
Write a compound inequality
Answer: $20 <= X < = $21
Step-by-step explanation:
According to the question, you are told that he loses by going over $21 or by buying all items and being less than $20.
That means the total amount of the items bought must be equal to 20 dollars or 21 dollars or be within the two amount of money.
If Mikel buys six bottles of shampoo, let x represent the total amount for the six bottles of shampoo. Then, the compound inequalities for this expression will be x less than or equal to 21 dollars and x greater than or equal to 20 dollars. That is,
$20 <= X < = $21
A farmer has the same number of chickens, cows and goats. Together, all these animals have 210 legs. How many chickens live on this farm?
Answer:
21
Step-by-step explanation:
Chickens - 2x
cows - 4x
goats = 4x
2x+4x+4x+210
10x=210
x=21
CHECK:
21 chickens = 42 legs
21 cows = 84 legs
21 goats = 84 legs
42+84+84=210 legs
how do you solve this
Answer:
[tex](a).\:\:\int _1^{-1}3f\left(x\right)dx\:=-12[/tex] is the final answer.
Step-by-step explanation:
See the attachment below.
Best Regards!
HELLPPPPPApart from vehicle insurance, there are several other types of insurance such as life insurance, homeowner’s insurance, etc. The coverages for these types of insurances are mostly the same.
Answer:
Banks require home insurance all the way until the house is payed off. This also goes as far as things like taxing, government funding, and collecting money.
EXPERTS ONLY its not 0 or 128 In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16384
Step-by-step explanation:
Given, Total jars = 4
Total marbles = 7
Since we need to put marbles in 4 different jars, we need to choose a jar each time.
Possible choices for jars =4
Number of time we need to choose = number of marbles
So, by fundamental counting principle, we have
Total ways to put 7 marbles in 4 jars = [tex]4\times4\times 4\times 4\times4\times 4\times 4[/tex]
[tex]=4^7\\\\=16384[/tex]
Hence, the required number of ways =16384
In circle C, what is mArc F H?
Answer:f
Step-by-step explanation:
Answer: 31 degrees
Step-by-step explanation:
ordered pair please help
Answer:
PLS PLS DO MARK MY ANSWER AS THE BRAINLIEST......
Step-by-step explanation:
P - ( 2, -3) - 4TH QUADRANT
Q - (-3,-2) - 3RD QUADRANT
R - (1,3) - 1ST QUADRANT
S -(-2,2) - 2ND QUADRANT
Answer:
P - ( 2, -3) - 4TH QUADRANT
Q - (-3,-2) - 3RD QUADRANT
R - (1,3) - 1ST QUADRANT
S -(-2,2) - 2ND QUADRANT
Brendon is walking home from a place that is 1.5 miles away. The function y = 7,920 − 270x represents Brendon’s distance in feet from home, y, in relation to the number of minutes he walks, x. Bryan is also walking home. Every 15 minutes, he writes down the number of feet left to reach home, as shown in the table.
Minutes
Feet
0
8,000
15
3,800
Which statements about this situation are true?
Brendon walks faster.
Bryan walks faster.
Brendon and Bryan walk at the same speed.
Brendon was farther away from home when he started walking.
Bryan was farther away from home when he started walking.
Brendon and Bryan were an equal distance from home when they started walking.
Answer:
Bryan walks faster
Bryan was farther away from home when he started walking.
Step-by-step explanation:
Given the following :
Brendon's distance in feet from home 'y' in relation to the number of minutes walked 'x'
y = 7,920 − 270x
For bryan:
Minutes (x) - - - 0 - - - - - 15
Feet ( y) - - 8000 - - - 3800
General form of a linear equation :
y = mx + C
m = gradient / slope
m = (y2 - y1) / (x2 - x1)
m = (3800 - 8000) / (15 - 0)
m = -4200 / 15 = - 280
Intercept 'c' = 8000 (where line intersect the y axis), (since y = 8000, when x = 0)
Therefore,
Bryan's model:
y = 8000 - 280x
Comparing both functions :
Bryan has a greater speed ( from the gradient)
Bryan was farther away from home when he started walking ( intercept )
Answer:
Answer:
Bryan walks faster
Bryan was farther away from home when he started walking.
Step-by-step explanation:
Given the following :
Brendon's distance in feet from home 'y' in relation to the number of minutes walked 'x'
y = 7,920 − 270x
For bryan:
Minutes (x) - - - 0 - - - - - 15
Feet ( y) - - 8000 - - - 3800
General form of a linear equation :
y = mx + C
m = gradient / slope
m = (y2 - y1) / (x2 - x1)
m = (3800 - 8000) / (15 - 0)
m = -4200 / 15 = - 280
Intercept 'c' = 8000 (where line intersect the y axis), (since y = 8000, when x = 0)
Therefore,
Bryan's model:
y = 8000 - 280x
Comparing both functions :
Bryan has a greater speed ( from the gradient)
Bryan was farther away from home when he started walking ( intercept )
Step-by-step explanation:
Which expression is equivalent to
9(x + 4)?
A. 36x
B. 13x
C. 13+9x
D. 9x+36
Answer:
[tex]\boxed{D. 9x + 36}[/tex]
Step-by-step explanation:
Hey there!
Given info
9(x + 4)
Solve!
9*x = 9x
9*4 = 36
Answer
9x + 36
D. 9x + 36
Hope this helps :)
Answer:
[tex] \boxed{9x + 36}[/tex]
Option D is the correct option.
Step-by-step explanation:
[tex] \mathrm{9(x + 4)}[/tex]
Distribute 9 through the parentheses
[tex] \mathrm{ = 9 x + 9 \times 4}[/tex]
Multiply the numbers
[tex] \mathrm{ = 9x + 36}[/tex]
Hope I helped!
Best regards!
The function f(x)=3(1.85)^x+3 is a shown .....
Answer:
easy, heres a hand y≈12⋅1.85x :)
P.s. have a good day :)
Answer:
see below
Step-by-step explanation:
f(x)=3(1.85)^x +3
Let x = - ∞
f(x)=3(1.85)^-∞ +3
= 3* 0 +3
= 3
The graph goes to 3
The graph has a horizontal asymptote of y=3
Let x = ∞
f(x)=3(1.85)^∞ +3
= 3* ∞ +3
= ∞
The graph goes to ∞
Kareem has scored 21 ,17 , and 25 points in his three basketball games so far. How many points does he need to score in his next game so that his average (mean) is 21 points per game?
Answer:
21
Step-by-step explanation:
his mean is already 21
but if he has to score then 21
What can a firm do to increase productivity in the short run once its marginal product is zero?
Increase the quantity of the input.
Decrease the quantity of the input.
Lower the price of its product.
Raise the price of its product.
Nothing, as more workers decreases total product.
Answer:
Decrease the quantity of the input
Step-by-step explanation:
The general assumption is that productivity is a curve that is concave downward, Hence marginal product is decreasing until it reaches zero. The way to increase it is to reduce the input quantity to a value below the point where the curve reaches zero marginal product.
Answer:
e) Nothing, as more workers decreases total product.
Step-by-step explanation:
I got it right on the test.
Find the value of x that makes s and t parallel.
3.
3(x-8)"
2(x + 10)"
I
Answer:
x=44
Step-by-step explanation:
If the lines were parallel, then those two angles would be equal since they are alternate interior angles. So:
3(x-8)=2(x+10)
3x-24=2x+20
x=44
Hope this is helpful! :)
Answer:
x=36.8
Step-by-step explanation:
We know that the two angles given are supplementary so we can do:
3(x-8)+2(x+10)=180
Then we simplify.
3x-24+2x+20=180
Simplify
5x-4=180
Combine like terms
5x-4=180
+4 +4
5x=184
Divide to make it x alone.
5x=184
/5 /5
x = 36.8
I hope this helped
Solomon needs to justify the formula for the arc length of a sector. Which expression best completes this argument?The circumference of a circle is given by the formula , where d is the diameter.Because the diameter is twice the radius, .If equally sized central angles, each with a measure of , are drawn, the number of sectors that are formed will be equal to _____.The arc length of each sector is the circumference divided by the number of sectors, or .Therefore, the arc length of a sector of a circle with a central angle of is given by or ... help please
Answer:
[tex]\frac{360}{n}[/tex]
Step-by-step explanation:
Given:
The above statements
Required
Complete the above statements
Considering the third statement in the question;
First, it should be noted that a circle is a full sector that measures 360 degrees
Assuming the circle is divided by a central angle of 180, the number of sectors formed will be;
[tex]\frac{360}{180} = 2\ sectors[/tex]
Further assume the circle is divided by a central angle of 90, the number of sectors formed will be;
[tex]\frac{360}{90} = 4\ sectors[/tex]
Similarly, if the circle is divided by a central angle of n, the number of sectors formed will be;
[tex]\frac{360}{n}[/tex]
Hence, from the list of given options; [tex]\frac{360}{n}[/tex] fills the gap correctly
Answer:
360/n
Step-by-step explanation:
How many different 2-digit numbers are there with the following property: the tenth digit is greater than the units digit?
Step-by-step explanation:
2 digit numbers are beetween 10 and 99
We are looking for numbers in wich the unit digits is less than the ten digit
we can make notice something about this numbers
1020304050607080900 is the smallest postive integer so all these numbers satisfy the condition
so we have now 9 numbers
here is another remark :
0 < 1 < 2 < 3 <4 <5 <6 < 7 < 8 < 9numbers from 91 to 99 satisfy the condition except 99
so here are 8 other numbers
numbers from 80 to 89 satisfy the condition except 88 and 89
so here are 7 other numbers
the numbers that satisfy the keeps decreasing by 1 each time
8 (91⇒98) 7 81⇒88 + 806 71⇒76 + 705 61⇒ 65 +604 51⇒ 54 + 50 3 41⇒ 43 + 402 31⇒32 + 301 21 + 20so the total number of numbers that satisfy the condition
9+8+7+6+5+4+3+2+1= 45
An expression is shown below: 2x3y + 18xy − 10x2y − 90y Part A: Rewrite the expression by factoring out the greatest common factor. Part B: Factor the entire expression completely. Show the steps of your work.
Answer:
Part A : 2y( x³ + 9x - 5x² - 45 ), Part B : 2y( x - 5 )( x² + 9 )
Step-by-step explanation:
Part A : Let's break every term down here to their " prime factors ", and see what is common among them,
2x³y + 18xy − 10x²y − 90y -
2x³y = 2 [tex]*[/tex] x³ [tex]*[/tex] y,
18xy = 2 [tex]*[/tex] 3 [tex]*[/tex] 3 [tex]*[/tex] x [tex]*[/tex] y,
− 10x²y = 2 [tex]*[/tex] - 5 [tex]*[/tex] x² [tex]*[/tex] y, - so as you can see for this example I purposely broke down - 10 into 2 and - 5. I could have placed the negative on the 2, but as that value was must likely common among all the terms, I decided to place it on the 5. The same goes for " − 90y. " I placed the negative there on the 5 once more.
− 90y = 2 [tex]*[/tex] - 5 [tex]*[/tex] 3 [tex]*[/tex] 3 [tex]*[/tex] y
The terms common among each term are 2 and y. Therefore, the GCF ( greatest common factor ) is 2x. Let's now factor the expression using this value.
2y( x³ + 9x - 5x² - 45 )
Part B : Let's simply factor this entire expression. Of course starting with the " factored " expression : 2y( x³ + 9x - 5x² - 45 ),
[tex]2y\left(x^3+9x-5x^2-45\right)[/tex] - Factor out " [tex](x^3+9x-5x^2-45\right))[/tex] " by grouping,
[tex]\left(x^3-5x^2\right)+\left(9x-45\right)[/tex] - Factor 9 from 9x - 45 and x² from x³ - 5x²,
[tex]9\left(x-5\right)+x^2\left(x-5\right)[/tex] - Factor out common term x - 5,
[tex]\left(x-5\right)\left(x^2+9\right)[/tex] - And our solution is thus 2y( x - 5 )( x² + 9 )
*PLEASE ANSWER ASAP* What is the area of this polygon on a coordinate plane?
Answer:
A. 14 square units
Step-by-step explanation:
Hey there :)
Well let's find the area of each individual rectangles.
Let's start with the side rectangle.
It has dimensions of 5*1 = 5.
5 square units
Now the 3 rectangles left have dimensions of 3*1=3,
3*3 = 9.
5+9=14
14 square units
Answer:
A, 14 square units
Step-by-step explanation:
What I would do is separate them into 4 shapes like the picture below
Because all of the shapes are rectangles, you can use the formula
[tex]A=L*W[/tex]
For shape #1, the length is 1 and the width is 3. Plot the numbers
[tex]A=1*3[/tex]
Multiply 1 by 3 to get
[tex]A=3[/tex]
The area of shape #1 is 3
The length and width of shape #2 and 3 are the same as 1, so you can multiply the area of shape #1 by 3 to get
[tex]3*3[/tex]
[tex]9[/tex]
The area of shape #1, 2, and 3 are 9.
Next, you want to find the area of shape #4 which has a length of 5 and a width of 1.
Use the same formula to get
[tex]A=5*1[/tex]
Multiply 5 by 1 to get
[tex]A=5[/tex]
The area of shape #4 is 5
The way to find the surface area of the whole figure is to add the area of all the shapes individually, or do what I did and add 5, to 9
[tex]A=5+9[/tex]
This gives you your answer which is
[tex]A=14[/tex]
Hope this helps.
Feel free to ask any more questions if you are confused.
Have a great day! :)
Which congruence theorems can be used to prove ΔEFG ≅ ΔJHG? Select two options.
Triangles E F G and J H G are connected at point G. Sides F G and and G H are congruent. Sides E F and H J are parallel.
HL
SAS
SSS
ASA
AAS
ASA and AAS
Step-by-step explanation:
We do not know if these are right triangles; therefore we cannot use HL to prove congruence.
We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.
We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.
Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.
The congruence theorems that can be used to prove ΔEFG ≅ ΔJHG are; ASA and AAS
It is impossible to know if these are right triangles from the information given;
On this note, only one side of each triangle is marked congruent;
Hence, we are unable use SSS or SAS to affirm congruence.
Additionally, since EF is parallel to HJ. Therefore, line EJ is a transversal. This also means that ∠HJG and ∠GEF are alternate (z-angles) interior angles and are therefore congruent. Similarly, ∠EGF and ∠HGJ are vertical angles and are congruent. We have therefore established the AAS congruence theorem.Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate (z-angles) interior angles and are congruent. Similarly, ∠EGF and ∠HGJ are vertical angles and are congruent; This gives us two angles and an included side, which is the ASA congruence theorem.Read more on congruence theorems:
https://brainly.com/question/2102943
Sarina orders a sixteen-inch diameter pizza. She divides it
into equal slices by cutting every thirty degrees around the
middle of the pizza. Approximately what is the area of each
slice?
Answer: c) 16.75 in²
Step-by-step explanation:
Area of a sector = π·r² (θ/360°)Given: diameter = 16 --> r = 8, θ = 30°
[tex]A=\pi (8)^2\bigg(\dfrac{30^o}{360^o}\bigg)\\\\.\quad =\dfrac{64\pi}{12}\\\\.\quad =\dfrac{16\pi}{3}\\\\.\quad = 16.755[/tex]
The diagonals of a parallelogram are 24 meters and 40 meters and
intersect at an angle of 60o. Find the length of the longer side.
Answer:
28 m
Step-by-step explanation:
The longer side can be found using the Law of Cosines. The semi-diagonals are of length 12 and 20 m, and the angle between them facing the long side is 180° -60° = 120°.
c^2 = a^2 +b^2 -2ab·cos(C)
c^2 = 12^2 +20^2 -2·12·20·cos(120°) = 144 +400 +240 = 784
c = √784 = 28
The longer side is 28 meters.
*PLEASE ANSWER* Which of the following is not a step in finding the area of an unknown figure? a.) Expand the figure and stretch it to the form of a known figure. b.) Divide the figure into smaller, known figures. c.) Add up the areas of the smaller figures. d.) Calculate the areas of the smaller figures.
Answer:
a.) Expand the figure and stretch it to the form of a known figure.
Step-by-step explanation:
"Option a" is the correct one for finding the area of unknown figure we don't expand and stretch the figure to form a known figure.
Steps for finding the area of unknown figureTo find the area of unknown shapes, first , we need to divide the unknown shapes into regular shapes that you can recognize such as triangles, rectangles, circles, squares and so forth.
Then find the area of these individual shapes and add them to get an area of unknown shapes.
According to the given question
We have to find the step which is not required for finding the area of unknown figures
"For finding the areas of unknown figure we don't need to stretch it to form a known figure" because if we expand and stretch the figure it's dimensions will get change so that the area will also gets change.
Hence," option a" is not a step in finding the area of unknown figure.
Learn more about the area of unknown figure here:
https://brainly.in/question/43346864
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