The following equation simplified by factoring or distributing:
2x + 62x + 6 + 2y-10x + 1540w - 5p4(5 + 8w)12(7 + 3z)12(7 + 3z)4y² - 38y - 20Factorization1.) 2(x + 3)
= 2x + 6
2.) 2(x + 3 + y)
= 2x + 6 + 2y
3.) −5 (2x − 3)
= -10x + 15
4.) –5(–8w + p)
= 40w - 5p
5.) 20 + 32w
= 4(5 + 8w)
6.) 84 + 36z
= 12(7 + 3z)
7.) (2x - 6)(5x + 7)
= 10x² + 14x - 30x - 42
= 10x² - 16x - 42
8.) (y - 10)(4y + 2)
= 4y² + 2y - 40y - 20
= 4y² - 38y - 20
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Colin found 22 more mushrooms that sophie did while they were out picking them in the forest. On the way home Sophie asked Colin to give her mushrooms so they have equal amounts. How many mushrooms did Colin give to Sophie?
Answer:
11 mushrooms
Step-by-step explanation:
Let's take two sets of numbers that fulfill the requirements (2 and 24 | 5 and 27)
In the first case, there are 26 mushrooms, and to have an equal amount they each need 13. Collin had to give 11 mushrooms to Sophie.
In the second case, there are 32 mushrooms, and they both need 16 each. So in this case, Collin also had to give 11 to Sophie.
The answer is 11 mushrooms.
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
The expression square root of 25/49 can be given as 5/7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is the non equal comparison of two or more numbers and variables.
The solution to the system of inequalities x – 4y < 4 and y < x + 1 is shown in the graph.
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Answer:
its c
Step-by-step explanation:
Fill in the digit on the right side of each equation so that each equation has an integer solution.
A) 35x−11=107....
B)9m+34=68....
C)7965−4m=19....
20 pts
The digit on the right side of each equation so that each equation has an integer solution are 2.74, 3.78 and 1986.5 respectively.
Equation35x - 11 = 107
35x = 107 - 11
35x = 96
x = 96/35
x = 2.74
9m + 34 = 68
9m = 68 - 34
9m = 34
m = 34/9
m = 3.78
7965 - 4m = 19
-4m = 19 - 7965
-4m = -7946
m = -7946/-4
m = 1986.5
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Provide the next step to derive the quadratic formula.
Step 1 : ax2+box+c=0
Step 2 : ax2+box=-c
Step 3 : x2 + b/ax=-c/a
Step 4 : ??
The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Step 1:
ax² + bx + c = 0
Step 2:
ax² + bx = -c
Step 3:
x² + (b/a)x = -c/a
Step 4:
x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)
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Please help me out :P
cos θ = [tex]\frac{-4\sqrt{65} }{65}[/tex], sin θ = [tex]\frac{-7\sqrt{65} }{65}[/tex], cot θ = 4/7, sec θ = [tex]\frac{-\sqrt{65} }{4}[/tex], cosec θ = [tex]\frac{-\sqrt{65} }{7}[/tex]
What are trigonometric ratios?Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin θ: Opposite Side to θ/Hypotenuse
Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos
Cos θ: Adjacent Side to θ/Hypotenuse
Sec θ: Hypotenuse/Adjacent Side & 1/cos θ
Analysis:
tan θ = opposite/adjacent = 7/4
opposite = 7, adjacent = 4.
we now look for the hypotenuse of the right angled triangle
hypotenuse = [tex]\sqrt{7^{2} + 4^{2} }[/tex] = [tex]\sqrt{49+16}[/tex] = [tex]\sqrt{65}[/tex]
sin θ = opposite/ hyp = [tex]\frac{7}{\sqrt{65} }[/tex]
Rationalize, [tex]\frac{7}{\sqrt{65} }[/tex] x [tex]\frac{\sqrt{65} }{\sqrt{65} }[/tex] = [tex]\frac{7\sqrt{65} }{65}[/tex]
But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.
Therefore, sin θ = - [tex]\frac{7\sqrt{65} }{65}[/tex]
cos θ = adj/hyp = [tex]\frac{4}{\sqrt{65} }[/tex]
By rationalizing and knowing that cos θ is negative, cos θ = -[tex]\frac{-4\sqrt{65} }{65}[/tex]
cot θ = 1/tan θ = 1/7/4 = 4/7
sec θ = 1/cos θ = 1/[tex]\frac{4}{\sqrt{65} }[/tex] = -[tex]\frac{-\sqrt{65} }{4}[/tex]
cosec θ = 1/sin θ = 1/[tex]\frac{\sqrt{65} }{7}[/tex] = [tex]\frac{-\sqrt{65} }{7}[/tex]
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Need help with Matrices!!
Find the length of JH help pls
Answer:
19 units
Step-by-step explanation:
JM is 40 units, and it is composed of JH and HM. HM is 21 units, and so JH must be the remaining units.
40 - 21 = 19
Brainliest, please :)
HELP QUICKLY PLEASE!!!!!!!!
Answer: 20
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{?}{16}=\frac{15}{12}[/tex]
Now, we will cross-multiply.
12 * ? = 16 * 15
12? = 240
? = 20
Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -x+5
Answer: C. Y = 5x + 5
Step-by-step explanation:
We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.
First, we will find our slope. We will use [tex]\frac{rise}{run}[/tex] for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.
-> Slope = 5
Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.
-> Y-intercept = 5
Lastly, we will write our equation and decide on an answer.
y = mx + b
y = (5)x + (5)
Y = 5x + 5
C. Y = 5x + 5
find the exact value
By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].
How to find the exact value of a trigonometric expression
Trigonometric functions are trascendent functions, these are, that cannot be described algebraically. Herein we must utilize trigonometric formulae to calculate the exact value of a trigonometric function:
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }[/tex]
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }[/tex]
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }[/tex]
[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{2+\sqrt{3}}{4} }[/tex]
[tex]\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].
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For f(x)=4x+1 and g(x) = x^2 - 5, find (f+g)(x).
Answer:
(f + g)(x) = x² + 4x - 4
Step-by-step explanation:
The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.
f(x) = 4x + 1
g(x) = x² - 5
(f + g)(x) <----- Original statement
f(x) + g(x) <----- Rewrite
(4x + 1) + (x² - 5) <----- Substitute the equations in f(x) and g(x)
4x + x² - 4 <----- Add 1 and -5
x² + 4x - 4 <----- Rearrange the terms
The line graph on the y-axis is parallel to the x-axis, 3rd quadrant point, and an open downward parabola.
can anyone help?
Answer:
[tex](x + 5) {}^{2} = - 12(y - 1)[/tex]
Triangles A B C and X Y Z are shown. Sides A C and Z X are congruent. Angles B A C and Z X Y are 35 degrees. Angle X Z Y is 47 degrees. Angle A B C is 98 degrees.
Determine the rigid transformations that will map ΔABC to ΔXYZ.
Translate vertex B to vertex Z; reflect ΔABC across side AB.
Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.
Reflect ΔABC across side AB; translate vertex C to vertex X.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
We know that the sum of angles of a triangle is always. In ΔXYZ,
What is the sum angle of the triangle?
[tex]\angle A + \angle B + \angle C=180^0[/tex]
[tex]35^0+\angle Y+47^0=180^0[/tex]
[tex]\angle y=98^0[/tex]
In both triangles, it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A=\angle X=35^0[/tex]and.[tex]\angle B = \angle Y =98^0[/tex]
By the AAS rule of congruence, ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having the same angle and rotate the triangle to align the sides and angles.
Since vertex X and vertex A have the same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.
Hence the correct option is d.
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Answer:
D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
Step-by-step explanation:
edge 2022
if a cake was sold GH 200 cedis. However, there is a reduction sale of 10% on each cake if you buy 4. Amanda decides to buy 8 cakes, how much would she pay
Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.
What is Cost Price?
Cost price is the amount we pay to buy an item at which it is available.
Here,
Selling price of a cake = 200 cedis
Discount because of sale = 10% on each unit.
(Only if 4 cakes purchased at a time)
Amanda purchased 8 cakes
So, Amanda need to pay only 90 percent of the total amount.
Total cost price of 8 cakes for Amanda = (200 X 90%) X 8
= 180 X 8
= 1440
Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.
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=Which composition of transformations will create a pair of similar, not congruent triangles?
a rotation, then a reflection
a translation, then a rotation
a reflection, then a translation
a rotation, then a dilation
Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.
Which composition of transformations will create a pair of similar, not congruent triangles?
In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.
Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.
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Answer:
D. a rotation, then a dilation
Step-by-step explanation:
got it right on edge 23
Which of the following is equivalent to the complex number i^36?
1
i
-1
-i
Answer:
1
Step-by-step explanation:
[tex]i^4=1\\\\i^{36}=(i^{4})^9=(1)^9=1[/tex]
Murder Rates The data represent the murder rate per 100,000 individuals in a sample of selected cities in the United States. Find the variance and standard deviation. Round your answers to at least one decimal place. Class limits Frequency 5-11 10 12-18 9 19-25 10 26-32 5 33-39 2 40-46 6
The Sample mean,Sample Variance, Standard deviation is mathematically given as
x=21.66[tex]\sigma=138.52[/tex][tex]\mu=11.769[/tex]What is the Sample mean,Sample Variance, Standard deviation.?Generally, the equation for Sample mean is mathematically given as
[tex]x = \frac{1}{N}(\sum xifi )[/tex]
Where
[tex]\sum xifi=80+135+220+145+72+258[/tex]
[tex]\sum xifi=910[/tex]
Therefore
x=1/42 (910)
x=21.66
Sample Variance
[tex]\sigma = \frac{1}{N-1}(\sum xi^2fi-(\frac{1}{N}(\sum xifi^2 )) )[/tex]
Where
[tex]\sum xi^2fi=640+2025+4840+4205+2592+11094[/tex]
[tex]\sum xi^2fi=25396[/tex]
Therefore
[tex]\sigma = \frac{1}{41}(25396-(\frac{1}{42}(910^2 )) )[/tex]
[tex]\sigma=138.52[/tex]
Standard deviation.
[tex]\mu=\sqrt{\sigma^2}\\\\\mu=\sqrt{138.52}[/tex]
[tex]\mu=11.769[/tex]
In conclusion,
x=21.66
[tex]\sigma=138.52[/tex]
[tex]\mu=11.769[/tex]
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CAN YALL PLEASE WORK IT OUTTT
$18.79 + $2.11 + ‐$1.92 + $17.28
Answer:
40.1
Step-by-step explanation:
Because the order of operations (Bodmas or Pedmas) tells you to add from left to right. So you would do 18.79 + 2.11 = 20.9, then you would do 20.90 + 1.92 (Add 0 at the end of 20.9) = 22.81. Then you will add 22.81 + 17.28 = 40.1. So your answer is 40.1. Hope this helps!
what is the gradient?
please help
The gradient of line A is -2. 67
How to determine the gradient
Gradient = slope = Δy/ Δx
We have,
y2 = 3
y1 = -5
x2 = -3
x1 = 0
Substitute the values
Gradient = [tex]\frac{3 - (-5)}{-3 -0}[/tex]
Gradient = [tex]\frac{3 + 5}{-3}[/tex]
Gradient = [tex]\frac{8}{-3}[/tex]
Gradient = -2. 67
Thus, the gradient of line A is -2. 67
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To prove part of the triangle midsegment theorem using the diagram, which statement must be shown?
The length of JK equals the length of JL.
The length of GH is half the length of KL.
The slope of JK equals the slope of JL.
The slope of GH is half the slope of KL.
The statement which the diagram shows is that the length of GH is half of the length of KL . Option B
What is the midsegment theorem?
The midsegment theorem holds that any segment that forms the joining midpoints of two sides of a triangle is parallel to half the length of the third side.
It can be seen that the length of GH is half of the length of KL as deduced from the diagram
Therefore, the statement which the diagram shows is that the length of GH is half of the length of KL . Option B
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How do I even do this...
Answer:
x = 2 ± [tex]\sqrt{15}[/tex]
Step-by-step explanation:
x² - 4x - 11 = 0 ( add 11 to both sides )
x² - 4x = 11
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 2)x + 4 = 11 + 4
(x - 2)² = 15 ( take square root of both sides )
x - 2 = ± [tex]\sqrt{15}[/tex] ( add 2 to both sides )
x = 2 ± [tex]\sqrt{15}[/tex]
help me please 20 points
Answer:
28 square meters.
Step-by-step explanation:
The total area - the grass area = the cement area.
36 - 8 = 28.
28 square meters.
Giving 15 points for the answer.
Answer:
4p-3
Explaination
when we subtract
4p-3 -3p-6
it will give us p _9
When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE?
The question is incomplete. Please read below to find the missing content.
D) cumulative is an argument that should be set to FALSE.
If we use cumulative =fake then we are able to get a precise probability
If we use cumulative= genuine, we will get less than or equal to possibility.
A sequence of actions wherein the effects are always unsure. I was tossing a coin, deciding on a card from a deck of playing cards, and throwing a cube. occasion. It is a single final result of a test. Getting a Head at the same time as tossing a coin is an occasion.
When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE? Select an answer
A) number_s
B) probability_s
C) trials
D) cumulative
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Shota invests $2000 in a certificate of deposit that earns 2%, percent in interest each year.
Write a function that gives the total value V(t) in dollars, of the investment t years from now.
Answer:
[tex]2 * 10^3 * 1,02^t[/tex]
Step-by-step explanation:
Let [tex]S = 2000 = 2 * 10^3[/tex] dollars be our investment, [tex]r = 2\%[/tex] - our interest rate. In order to simplify things, I suggest bringing the variable [tex]p[/tex] into play: [tex]p = 1 + \frac{r}{100}[/tex]. So, after year [tex]1[/tex] we will have [tex]S_{1} = S + \frac{r}{100}S = S(1 + \frac{r}{100} ) = Sp[/tex]. After year [tex]2[/tex]: [tex]S_{2} = S_{1}p = Sp * p = Sp^2[/tex]. After year [tex]t[/tex]: [tex]S_{t} = S_{t - 1}p = Sp^t[/tex]. Besides, we can count [tex]p[/tex]. Indeed, [tex]p = 1 + \frac{r}{100} = 1 + \frac{2}{100} = \frac{100}{100} + \frac{2}{100} = \frac{102}{100} = 1,02[/tex]. Therefore, [tex]V(t) = Sp^t = 2 * 10^3 * 1,02^t[/tex].
8. In February 2018, a newspaper reported that the total land area of Singapore is expected to reach 76 600 hectares by 2030. This is an increase of about 6.4% from the total land area in 2017. Find the total land area in 2017, giving your answer correct to 4 significant figures.
Answer:
The answer is 7.199 x 10^4 hectares
Step-by-step explanation:
Let's set x as the total land area in 2017.
x * (1 + 6.4%) = 76,600
x * (1 + 0.064) = 76,600
x * 1.064 = 76,600
x = 76,600 / 1.064
x = 71,992.48
x = 7.199 * 10^4 hectares
help trigonometry
cccccc
Answer:
D
Step-by-step explanation:
Trigonometry ratios:[tex]\sf Sin \ \theta =\dfrac{opposite \ side }{hypotenuse} =\dfrac{12}{37}[/tex]
To find the adjacent side use Pythagorean theorem.
Opposite side² + adjacent side² = hypotenuse²
adjacent side² = hypotenuse² - opposite side²
= 37² - 12²
= 1369 - 144
= 1225
adjacent side = √1225
= 35
[tex]\sf tan \ \theta =\dfrac{Opposite \ side }{adjacent \ side}\\\\tan \ \theta = \dfrac{12}{35}[/tex]
please help its confusing me
Answer:
x=−9 and y=8
Step-by-step explanation:
Let's solve your system by elimination.
2x+3y=6;4x−y=−44
Multiply the first equation by -2,and multiply the second equation by 1.
−2(2x+3y=6)
1(4x−y=−44)
Becomes:
−4x−6y=−12
4x−y=−44
Add these equations to eliminate x:
−7y=−56
Then solve−7y=−56for y:
−7y=−56
-7y/-7 = = -56/-7
(Divide both sides by -7)
y=8
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
2x+3y=6
Substitute8 for y in 2x+3y=6:
2x+(3)(8)=6
2x+24=6(Simplify both sides of the equation)
2x+24+−24=6+−24(Add -24 to both sides)
2x=−18
2x/2 = -18/2 (Divide both sides by 2)
x=−9
Answer:
x=−9 and y=8
Answer:
x = -9
y = 8
Step-by-step explanation:
(using substitution)
4x-y = -44
4x + 44 = y
substitute (4x+44) as y in the other equation
2x + 3(4x+44) = 6
2x+12x+132 = 6
14x = -126
x = -9
then plug -9 as x into one of the equations to find y
4(-9) - y = -44
-36-y=-44
-y=-8
y=8
then check the answer by plugging in the values of x and y (-9 and 8) for x and y in one of the equations
4(-9) - (8) = -44
you get: -44 = -44, which is true, so the x and y values are correct
A grocery store sells 1 gallon containers of milk for 3.99. The store also sells orange juice in a 6 pack of 5.5 fluid ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?
The a gallon of orange juice will cost $ 3.0 more than a gallon of milk.
Size of the orange juiceThe size of the orange juice in gallon is calculated as follows;
1 ounce = 0.0078125 gal
5.5 ounce = ?
= 0.043 gallon
Total volume of 6 pack = 6 x 0.043 gal = 0.258 gal
0.258 gal = $1.79
1 gal = ?
= $ 6.94
Difference between cost of gallon of milk and orange juice= $ 6.94 - $ 3.99
= $2.95
≈ $ 3.0
Thus, the a gallon of orange juice will cost $ 3.0 more than a gallon of milk.
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How to work out this linear stimultaneous equations
Step-by-step explanation:
extract the third equation from one of the given equation by making at most one variable with 1 as the coefficient the subject of the equation.[tex] x = 2 - y...........(3)[/tex]now substitute the third equation to the other equation *Not the one you extracted the new equation from*[tex]y = 2 ({2 - y})^{2} + (2 -y ) - 2[/tex]After substituting simplify[tex]y = 2(2 - y)(2 - y) + 2 - y - 2 \\ y = 2(4 - 2y - 2y + {y}^{2} ) + 2 - y - 2 \\ y = 2(4 - 4y + {y}^{2} ) - y \\ y = 8 - 8y + 2 {y }^{2} - y[/tex]Therfore group the terms in the form of a general Quadratic equation.