The greatest common factor or GCF in the expression 4y + xy² + 6y is y.
The given expression is 4y + xy2 + 6y
GCF stands for greatest common factor
Among these three numbers ;
the variable y is common in all three of them
The factors of 4 y = 4 and y
the factors of xy² are x and y
and the factors of 6y are 6 and y
This can also be simply written by taking y common in this
for example; y ( 4 + xy + 6 )
From the above mentioned proof we can establish the fact that the variable y is common in all three of them
Thus the greatest common factor among them is y
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8) -14x-7y - 18
-6x-3y-6
I need help badly
Can you help me with this one please? Only part b
Simplifying,
[tex]\begin{gathered} ((5+2i)^2-2)i\rightarrow(25+20i+4i^2-2)i\rightarrow(23+20i-4)i \\ \\ \rightarrow(19+20i)i\rightarrow19i+20i^2\rightarrow-20+19i \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
For f(x) and g(x), describe each transformation. Then write the equation of the transformed function. f(x)=2x+1 g(x)=1/3x+2
I am haveing a very hard time figuring this out due to my dyscalculia
The transformation processes and equation of the transformed function are:
a) f(x) is translated in the negative y direction and the equation of the transformed function is f(x) = 2x - 4
b) g(x) is translated in the positive y direction and the equation is g(x) = 1/3x + 6
c) g(x) is dilated 3 times hat it as and the equation is x + 6
d) f(x) is dilated and the equation is x + 1/2
What is Dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
f(x) is translated by 5 units to the negative y-direction, so f(x) - 5 becomes 2x + 1 -5 = 2x - 4
g(x) + 4 means translation 4 units to the positive y-axis and the function g(x) + 4 becomes x/3 + 2 + 4 = x/3 + 6
3g(x) is dilation which means g(x) would be 3 times what it was initially.
3 x ( x/3 + 2) = x + 6
1/2f(x) is dilation which is a reduction by half. so the function becomes
1/2 x ( 2x + 1) = x + 1/2
In conclusion, the transformation processes are:
a) f(x) is translated in the negative y direction and the equation of the transformed function is f(x) = 2x - 4
b) g(x) is translated in the positive y direction and the equation is g(x) = 1/3x + 6
c) g(x) is dilated 3 times hat it as and the equation is x + 6
d) f(x) is dilated and the equation is x + 1/2
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Maddie borrowed $1500 at a 4% interest rate. If she pays off the loan in 3 years.
how much will she pay in total with interest?
$1,680
$50
$500
$180
Answer:
1680
Step-by-step explanation:
Answer:
I guess if she is Pays the money in three years, she will pay a capital of 1500/3 per year, which is 500$ per year. The Interest she pays the first year is: I=Debt*interest rate, so I=1500$*0.04, which is: I=60$. So without other information, i assume she pays 60$ each year, so in three years: I=60*3 --> 180$.
Solve the inequality
6(x/2+4)≥9
3x+24=9
3x=9-24
3x=-15
x=-5
which of the following expression is equivalent to 7 y + 21 y(7+21) 7(y+21). 7(y+3. 21y+7
The expression given is;
[tex]\begin{gathered} 7y+21 \\ \text{The equivalent is;} \\ =7(y+3) \\ We\text{ use 7 to factor both sides of the expression, hence} \\ \frac{7y}{7}=y \\ \text{And} \\ \frac{21}{7}=3 \\ \text{Therefore, the answer is } \\ 7(y+3) \end{gathered}[/tex]The correct answer is option C
Josiah scored 63 points by collecting 3 coins. After collecting a total of 4 coins, how many points will Josiah have scored in all?
Answer: 84 points
Step-by-step explanation:
There are two ways I see that you can solve this.
In the first method, we can find the points per coin. To do this, we divide 63/3 and we get 21.
63/3=21
Now we know that in 1 coin, there is 21 points.
1 coin=21 points
Next, since we have to find the total amount of points in 4 coins. We multiply 21 by 4.
21*4=84 points
We do this because in 1 coin there is 21 points, and there is not 21 points in 4 coins. So when we multiply 21 and 4, we get 84 points, and 84 points is our answer.
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Another way you could do this would be to use cross multiplication. In cross multiplication, we would set up our work like this:
63/3=x/4 or in ratio way 3 : 63 = 4 : x
When you look at the ratio formation, you can easily tell that it says 3 to 63 is the same as 4 is to x. This can be written in the fraction formation, making it able for us to cross multiply. When we write it the fraction way, we write
63 x
____ = ____
3 4
With this, we do what the name says, we cross the numbers over and multiply, so we do 63*4=3*x
This way can be harder we have bigger numbers, but we can always simplify before multiplying, like in this case-
We can divide the 3 from both sides
63 * 4
_____ = x
3
From this we can simplify the 63 and 3, and so we would cancel out the 3 and would be left with 21*4=x
And this is the same equation we ended up with before.
So when we solve, we get 84=x and so the amount of points Josiah will have is 84 points.
What is the total surface area ratio of following similar solids?30 mi45 mi60 mi90 mi09:4O 15:6O 5:4O 3:2
Solid A has five(5) rectangular blocks that are co-joined. The dimension of each, is 45miles by 90miles.
Thus,
[tex]\begin{gathered} Total\text{ surface area=5}\times Area\text{ of one rectangular block} \\ \text{Total Surface Area=5}\times(45\times90) \\ T\mathrm{}S\mathrm{}A=5\times4050 \\ T\mathrm{}S\mathrm{}A=20250mi^2 \end{gathered}[/tex]Solid B has five(5) rectangular blocks that are co-joined. The dimension of each, is 30mi by 60mi.
Thus,
[tex]\begin{gathered} \text{Total Surface Area= 5}\times Area\text{ of one rectangular block} \\ T\mathrm{}S\mathrm{}A=5\times(30\times60) \\ T\mathrm{}S\mathrm{}A=5\times1800 \\ T\mathrm{}S\mathrm{}A=9000mi^2 \end{gathered}[/tex]The ratio of the T.S.A of the similar solids is given below:
[tex]\begin{gathered} T\mathrm{}S\mathrm{}A_{solid\text{ A}}\colon T.S.A_{solid\text{ B}} \\ 20250\colon9000 \\ \text{Divide both by 2250, we have:} \\ 9\colon4 \end{gathered}[/tex]Hence, the correct option is Option A
if two cubes have a ratio of 5:3, what is the ratio of their respective volumes? and if two cones have heights in the ratio d:c, what is the ratio of their respective volumes?
SOLUTION:
(a) We want to find the ratio of the volumes of the cubes,
5 x 5 x 5 = 125
3 x 3 x 3 = 27
125 : 27
(b) Since the two cones are similar, the ratio of the heights will be the same as the ratio of the radii, which means that the ratio of the volume will be;
[tex]d^{3\text{ }}\colon c^3[/tex]Use the model of the rectangular prism to answer the question. The width of the
prism is (2x - 2) ft, and its height is (x + 7) ft. The area of the base of the prism is
(3x2 + 3x - 4) ft².
Could the length of b be (3x - 1) ft? Complete the explanation.
Answer:
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
Step-by-step explanation:
Given dimensions of a rectangular prism:
Width = (2x - 2) ftHeight = (x + 7) ftArea of the base = (3x² + 3x - 4) ft²The area of the base of a rectangular prism is the product of the width of the base and the length of the base.
To determine if length b could be (3x - 1) ft, multiply b by the width of the base of the prism.
[tex]\begin{aligned}\implies \sf Area\;of\;base&=\sf length \times width\\&=b \times (2x-2)\\&=(3x-1)(2x-2)\\&=3x(2x-2)-1(2x-2)\\&=6x^2-6x-2x+2\\&=6x^2-8x+2\end{aligned}[/tex]
Therefore, the length of b cannot be (3x - 1) as the area of the base when b is (3x - 1) is not equal to the given area of the base.
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
A scientist observes and counts 155 bacteria in a culture. Later, the scientist counts again and finds the number has increased as shown.
Answer:
You multiply 155 by 0.40 which is 40% and you get 62 then you add 62 to 155 and your final count of bacteria is 217
Step-by-step explanation:
how do I do this on a line?[tex]3 \ \textless \ 2x - 3 \leqslant 13[/tex]
Let the inequality:
[tex]3\text{ }<\text{ 2x - 3}\leq\text{ 13}[/tex]1. we add + 3 :
[tex]3\text{ +3}<\text{ 2x }\leq\text{ 13}+3[/tex]this is equivalent to :
[tex]6<\text{ 2x }\leq\text{ 1}6[/tex]we resolve for x ( we divide by 2) :
[tex]3<\text{ x }\leq8[/tex]that is the interval:
[tex](3,\text{ 8}\rbrack[/tex]on the real line, the interval is:
On the other hand, the inequality:
[tex]-2\text{ }<\frac{3+x}{4}\leq\text{ 3}[/tex]
1. Multiply by 4:
[tex]-8\text{ }<3+x\leq12[/tex]2. Add -3:
[tex]-11\text{ }that is the interval:[tex](-11,\text{ 9}\rbrack[/tex]
on the real line, the interval is:
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A developer wants to subdivide a rectangular lot into square pieces. The lot is 600m by 2400m. What is the largest possible square? need answer asap
The largest possible square is of side 600m.
Given, a developer wants to subdivide a rectangular lot into square pieces. The lot is 600m by 2400m.
We have to find the largest possible square.
Now, to find the largest possible square we have to find the HCF of 600 and 2400.
As, the HCF of 600 and 2400 is
HCF(600 , 2400) = 600
So, the largest possible square can be of the side 600m
Hence, The largest possible square is of side 600m
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Question 1(Multiple Choice Worth 2 points)
(Converting Between Systems MC)
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
Using the conversion method, 4.6228 meter ribbon we need for craft project.
In the given question,
For a craft project you need 182 inches of ribbon, but it is only sold by the meter.
We have to determine the amount of ribbon, in meters.
As given 1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter.
Firstly we know that inches, meters and centimeters all are units to measure the length.
Since we know that in 1 inch have 2.54 centimeters and 1 centimeters have 0.01 meter.
So we firstly convert the 2.54 centimeters in meter.
1 centimeter = 0.01 meter
2.54 centimeter = 2.54×0.01 meter
2.54 centimeter = 2.54×0.01 meter
2.54 centimeter = 0.0254 meter
So we can say that
1 inch = 0.0254 meter
We have to by 182 inches of ribbon. So
182 inches = 0.0254×182 meters
182 inches = 4.6228 meters
Hence, 4.6228 meter ribbon we need for craft project.
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A portion of a hiking trail slopes upward at about a 6° angle.To the nearest tenth of a foot, what is the value of x, thehiker's change in vertical position, if he has traveled a
In the given right triangle ABC
we have that
[tex]tan(C=\frac{AB}{AC}\text{ ----> by TOA}[/tex]substitute given values
[tex]\begin{gathered} tan(6^o)=\frac{x}{120} \\ \\ x=120*tan(6^o) \\ x=12.6\text{ ft} \end{gathered}[/tex]The answer is the option Bhow do I find all of the following that can be a counterexample for the statement below?
As we need to select counterexamples, we have to select all the options that make the statement x+2>7 a FALSE statement.
Then, we can rearrange:
[tex]\begin{gathered} x+2>7 \\ x>7-2 \\ x>5 \end{gathered}[/tex]We have to select all the options where x is NOT greater than 5: -2, 0, 3, 4.
The options -2, 0, 3, 4 have to be selected.
find the image of (-2,-9) after a reflection over the y-axis
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]
if a || b, m<2=63°, and m<9=105°, find the measure of missing angle m<1=?
Given:
a.) ∠9 = 105°
b.) ∠2 = 63°
Step 1: Determine the measure of ∠10.
∠9 and ∠10 are Supplementary Angles. This means that the sum of the two angles is equal to 180°.
From this, we generate the following equation:
[tex]\text{ }\angle9\text{ + }\angle10=180^{\circ}[/tex]Let's then now proceed to find out the measure of ∠10.
[tex]\text{ }\angle9\text{ + }\angle10=180^{\circ}[/tex][tex]\text{ }105^{\circ}\text{ + }\angle10=180^{\circ}[/tex][tex]\angle10=180^{\circ}\text{ - }105^{\circ}[/tex][tex]\angle10=75^{\circ}[/tex]Step 2: Determine the measure of ∠3.
∠10 and ∠3 are Alternate Exterior Angles. Under this, the two angles must be congruent.
[tex]\text{ }\angle3\text{ = }\angle10[/tex]Therefore,
[tex]\text{ }\angle3\text{ = }\angle10[/tex][tex]\text{ }\angle3=75^{\circ}[/tex]Step 3: Determine the measure of ∠1.
∠1, ∠2 and ∠3 are also Supplementary Angles. This means that the sum of the three angles is equal to 180°.
Thus, we generate the equation below:
[tex]\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}[/tex]Let's now find the measure of ∠1,
[tex]\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}[/tex][tex]\text{ }\angle1\text{ + }63^{\circ}\text{ + }75^{\circ}=180^{\circ}[/tex][tex]\text{ }\angle1\text{ + }138^{\circ}=180^{\circ}[/tex][tex]\text{ }\angle1\text{ }=180^{\circ}\text{ - }138^{\circ}[/tex][tex]\text{ }\angle1\text{ }=42^{\circ}[/tex]Therefore, the measure of ∠1 is 42°.
I dont understand the question
The dot plots show the distribution of the length, in centimeters, of 25 shark teeth for an extinct species of shark and the length, in centimeters, of 25 shark teeth for a closely related shark species that is still living.
Compare the two dot plots using the shape of the distribution, measures of center, and measures of variability. Use the situation described in the problem in your explanation.
Living species teeth is shorter than extinct species & large species teeth length is more concentrated.
Slope of the distribution:
For extinct species, the symmetric distribution
For living species, left -shaved distribution.
Measures of center:
For extinct species: mean = 3.02 cm
For large species: mean = 2.32 cm
Therefore living species teeth length is shorter than extinct species.
Measures of variability:
For extinct species: b = 6.015cm
For large species: b = 0.13 cm
Therefore large species teeth length is more concentrated.
Hence the answer is, living species teeth is shorter than extinct species & large species teeth length is more concentrated.
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?
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
Area of Irregular Shapes
Nov 03, 2-44:03 PM
Answer:
9
3
100 POINTS PLEASE HELP !!!!!
Answer:
50.3 square units
Step-by-step explanation:
area of rectangle: 11 x twice the radius
radius = 2
A(rect): = 11(4) = 44 sq units
A (semi-circle) = (π·r²) / 2
A = 4π / 2 = 2π = 6.28 sq units
44.0 + 6.28 = 50.28
Answer:
68.1
Step-by-step explanation:
3.14*3²=28.26
28.26/2=14.13
3*2=6
9*6=54
54+14.13=68.13
68.1
Write the equation in Slope-Intercept form that passes through the point (-4, -9) and has a slope of 1/12.
Answer:
[tex]y=\frac{1}{12}x-\frac{26}{3}[/tex]
Step-by-step explanation:
[tex]y+9=\frac{1}{12}(x+4) \\ \\ y+9=\frac{1}{12}x+\frac{1}{3} \\ \\ y=\frac{1}{12}x-\frac{26}{3}[/tex]
what is the slope of a line that passes through the two points (8,3) nd (4,9)?
Given the points (8,3) and (4,9), we can find the slope of the line that passes through them with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, we have the following:
[tex]undefined[/tex]I need help with this question. I don’t know how to do this.
Solution:
The arithmetic sequence is given below as
[tex]19,24,29,34,...[/tex]Step 1:
We will calculate the common difference using the formula below
[tex]\begin{gathered} d=t_2-t_1=t_3-t_2 \\ d=24-19=29-24 \\ d=5 \end{gathered}[/tex]Step 2:
We will calculate the fifth term using the formula below
[tex]\begin{gathered} c \\ n=5,a=19,d=5 \\ t_5=19+(5-1)5 \\ t_5=19+20 \\ t_5=39 \end{gathered}[/tex]We will calculate the sixth term using the formula below
[tex]\begin{gathered} t_n=a+(n-1)d \\ n=6,a=19,d=5 \\ t_6=19+(6-1)5 \\ t_6=19+25 \\ t_6=44 \end{gathered}[/tex]We will calculate the seventh term using the formula below
[tex]\begin{gathered} t_7=a+(n-1)d \\ n=7,a=19,d=5 \\ t_7=19+(7-1)5 \\ t_7=19+30 \\ t_7=49 \end{gathered}[/tex]Hence,
The next three terms of the arithmetic sequence are given below as
[tex]\Rightarrow39,44,49[/tex]There is a line that includes the point (4, 6)
and has a slope of 1. What is its equation in
slope-intercept form?
Answer: y=x+2
Step-by-step explanation:
y-6=1(x-4)
y-6=x-4
y=x-4+6
y=x+2
25 over 23 as a decimal rounded to the nearest hundredth
Answer:
1.09
Step-by-step explanation:
25/23 is the same thing as 25 divided by 23
Once you get answer round to nearest hundreth
need some help pls due date 10pm
thanks to whoever answers
Answer:
x = 90°
y = 20°
z = 20°
Step-by-step explanation:
Each interior angle of a square is 90°.
Angles on a straight line sum to 180°.
Angle x
⇒ 90° + x = 180°
⇒ 90° + x - 90° = 180° - 90°
⇒ x = 90°
Angle z
⇒ z + 90° + 70° = 180°
⇒ z + 160° = 180°
⇒ z + 160° - 160° = 180° - 160°
⇒ z = 20°
Interior angles of a triangle sum to 180°.
Angle y
⇒ x + 70° + y = 180°
⇒ 90° + 70° + y = 180°
⇒ 160° + y = 180°
⇒ 160° + y - 160° = 180° - 160°
⇒ y = 20°
Angela and Barry share a piece of land. The ratio of the area of Angela’s portion to the
area of Barry’s portion is 3:2. They each grow corn and peas on their piece of land. The
entire piece of land is covered by corn and peas in the ration 7:3. On the Angela’s portion
of the land, the ratio of corn to peas is 4:1. What is the ratio of corn to peas for Barry’s portion?
(A)11:9 (B)2:3 (C)3:2 (D)3:7 (E)1:4
Answer:
3:2
Step-by-step explanation:
Angela + Barry = land
7 corn + 3 peas = land
4 corn + 1 peas = Angela
land = land
Angela + Barry = 7 corn + 3 peas
4 corn + 1 peas + Barry = 7 corn + 3 peas
Barry = 7 corn + 3 peas - 4 corn - 1 peas
Barry = 3 corn + 2 peas
Barry = 3:2
The ratio of corn to peas for Barry's portion is 3:2. Hence, option C is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data given in the question,
Angela + Barry = land
7 corn + 3 peas = land
4 corn + 1 peas = Angela
land = land
Angela + Barry = 7 corn + 3 peas
4 corn + 1 peas + Barry = 7 corn + 3 peas
Barry = 3 corn + 2 peas
Barry = 3:2
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