Answer:
C) 4x + 5yStep-by-step explanation:
[tex]\dfrac{2}{3}(3x+9y)+\dfrac{1}{2}(4x-2y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)(3\!\!\!\!\diagup^1x})+\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)(9\!\!\!\!\diagup^3y})+\left(\dfrac{1}{2\!\!\!\!\diagup_1}\right)(4\!\!\!\!\diagup^2x})+\left(\dfrac{1}{2\!\!\!\!\diagup_1}\right)(-2\!\!\!\!\diagup^1y})\\\\=2x+(2)(3y)+2x-y=2x+6y+2x-y\qquad\text{combine like terms}\\\\=(2x+2x)+(6y-y)=4x+5y[/tex]
Find the surface area of a square pyramid with a length of 5 cm and a slant height of 8 cm
Answer:
105 square cm.
Step-by-step explanation:
The surface area of a square pyramid is
[tex]SA=A_{base}+4A_{lateral \ side}.[/tex]
1. The base is the square with side length of 5 cm, thus
[tex]A_{base}=5\cdot 5=25\ cm^2.[/tex]
2. The lateral side is the triangle with the base of 5 cm and the height of 8 cm. Thus,
[tex]A_{lateral \ side}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}=\dfrac{1}{2}\cdot 5\cdot 8=20\ cm^2.[/tex]
Now, the surface area of the pyramid is
[tex]SA=25+4\cdot 20=105\ cm^2.[/tex]
Answer:
The surface area of a square pyramid is: 105 cm^2
Step-by-step explanation:
The surface area of a pyramid is given by the following formula
[tex]A = l ^ 2 + 4 * (0.5) lh[/tex]
Where
l is the length of one of the sides of the square base
h is the height of the pyramid
We know that h = 8 cm and l = 5 cm
[tex]A = 5 ^ 2 + 4 * (0.5) * 5 * 8\\\\A = 25 + 2 * (40)\\\\A = 105\ cm ^ 2[/tex]
A right rectangular prism is sliced parallel to its
base as shown in the figure.
What is the shape of the resulting two-
dimensional cross section?
Select from the drop-down menu to correctly complete the statement
The shape of the resulting two-dimensional
cross section is a Choose...
Pentagon
Rectangle
Trapezoid
Triangle
Answer:
the correct answer is rectangle
Step-by-step explanation:
The given line passes through the points (0, -3) and (2, 3).
on
What is the equation, in point-slope form, of the line that is
parallel to the given line and passes through the point
(-1,-1)?
y+1= (x + 1)
(23)
-
N
54-3-2-1
2
3 4
5
(0, -3)
Mark this and return
Save and Frit
Answer:
[tex]y+1=3(x+1)[/tex]
Step-by-step explanation:
step 1
Find the slope of the given line
[tex]m=(3+3)/(2-0)[/tex]
[tex]m=3[/tex]
step 2
Find the slope of the line that is parallel to the given line
we know that
If two lines are parallel, then their slopes are the same
therefore
the slope is equal to [tex]m=3[/tex]
step 3
Find the equation in point slope form
we have
[tex]m=3[/tex]
[tex]point (-1,-1)[/tex]
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y+1=3(x+1)[/tex] ----> equation of the line into point slope form
(4a^2-3b^2)(16a^4+12a^2b^2+9b^4)
Answer:
The correct answer is 64a^6 - 27b^4
Step-by-step explanation:
It is given an expression,
(4a^2 - 3b^2)(16a^4 + 12a^2b^2 + 9b^4)
To find the correct answer
(4a^2 - 3b^2)(16a^4 + 12a^2b^2 + 9b^4) can be written as,
(4a^2 - 3b^2)(16a^4 + 12a^2b^2 + 9b^4) = 4a^2 * (16a^4 + 12a^2b^2 + 9b^4) - 3b^2(16a^4 + 12a^2b^2 + 9b^4)
= 64a^6 + 48a^4b^2 + 36a^2b^4 - 48a^4b^2 - 36a^2b^4 - 27b^4
= 64a^6 - 27b^4 + 48a^4b^2 - 48a^4b^2 + 36a^2b^4 - 36a^2b^4
= 64a^6 - 27b^4
Therefore the correct answer is 64a^6 - 27b^4
Answer:
[tex]64a^6-27b^6[/tex]
Step-by-step explanation:
Hope this helps:) Have a good day!!
given vector u = (6,-4) and the graph of vector v, find v - 2u and express the result of terms in i and j
Answer:
0i + 10j, or just 10j
Step-by-step explanation:
Vector u = <6, -4> and vector v = <12, 2>.
We are to find v - 2u, which is:
<12, 2> - 2<6, -4>. We combine x components and y components to obtain:
<12-12, 2+8>, or <0, 10>.
In terms of i and j, that'd be 0i + 10j, or just 10j.
Answer:
v-2u=10j
Step-by-step explanation:
The component of vector v, are
u=<6,-4>
From the graph; vector u, has components.
v=<12,2>
We perform the subtraction;
v-2u=<12,2>-2<6,-4>
We multiply out the scalar to get:
v-2u=<12,2>-<12,-8>
This implies that;
v-2u=<12-12,2--8>
v-2u=<0,10>
v-2u=0i+10j
v-2u=10j
Calvin evaluated -2/3 *5 1/6 using the steps below.
The error is identified in C. In step 2, he confused the multiplication and addition signs.
What is Calvin's error?
In step 2, he confused the multiplication and addition signs.
Step 1: -2/3 x (5 + 1/6)
Step 2: (-2/3 × 5) + (-2/3 × 1/6)
Step 3: -10/3 + -12/18
Step 4: -10/3 - 2/3
= (-10-2)/3
= -12/3
= -4
Therefore,
Calvin's answer should be negative 4
Complete Questiion:
Calvin evaluated -2/3 x 5 1/6 using the steps below.
Step 1: -2/3 x (5 + 1/6)
Step 2: (-2/3 + 5)x(-2/3 + 1/3)
Step 3: 4 1/3 x -1/3
Step 4: -2 1/6
Which describes Calvin’s error?
In step 1, he incorrectly broke up 5 1/6.
In step 2, he distributed the -2/3 instead of the 5.
In step 2, he confused the multiplication and addition signs.
In step 3, he computed the addition and multiplication incorrectly
Name same side interior
Same side interior means that they have to be the angles inside the two parallel lines and on the same side
Look at the image below
The ones circled in pink is one set of same side interior and the ones in read are another
Hope this helped!
btw Only one of them is in the answer choices, but both are correct.
Answer:
The correct answer is last option
<3 and <5
Step-by-step explanation:
From the figure we can see that,
MP ║ JL and KN is the traversal
To find the same side interior
From figure we get,
same side interior angles are,
1). <3 and < 5
2). <4 and <6
From the given options the correct option is last option
<3 and <5
m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
Answer:
Final answer is x=23.
Step-by-step explanation:
Given that m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°
We know that sum of all three angles of a triangle equals 180 degree.
So we can write equation:
m∠A + m∠B + m∠C = 180°
60° +(3x − 2)° + (2x + 7)° = 180°
60 +3x − 2 + 2x + 7 = 180
67 +5x − 2 = 180
65 +5x = 180
5x = 180 - 65
5x = 115
[tex]x=\frac{115}{5}[/tex]
x=23
Hence final answer is x=23.
Solve the word problems using systems.
The sum of two numbers is 842. The difference is 314. Find the numbers.
Answer:
The numbers are 578 and 264
Step-by-step explanation:
Let
x-----> the greater number
y----> the smaller number
we know that
x+y=842 -----> equation A
x-y=314 -----> equation B
Adds equation A and equation B
x+y=842
x-y=314
------------
x+x=842+314
2x=1,156
x=578
Find the value of y
578+y=842
y=842-578=264
Rectangle
ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,1), B(5,1), C(5,6), and D(2,6).
Given these coordinates, what is the length of side
AB of this rectangle?
Answer:
3
Step-by-step explanation:
As we move from A(2, 1) to B(5, 1), x increases by 3 but y stays the same.
Thus, the distance from A to B is simply 3. This is the desired length.
The length of side AB would be 3 units,
As we move from A(2, 1) to B(5, 1), x increases by 3 but y stays the same.
Thus, the distance from A to B is simply 3. This is the desired length.
I recommend using Desmos to quickly graph things (it's much faster than doing it yourself, I use it often. You can graph points and everything).
The picture ends up looking like the attachment I have below.
This is now a simple subtraction.
A is at 2 on the x-axis and B is at 5.
5-2=3
3 units.
What are coordinate planes?
A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).
Learn more about the coordinate plane at
https://brainly.com/question/2689696
#SPJ2
What is the average rate of change of the function over the interval x = 0 to x = 4? f(x) = 2x - 1
Enter your answer in the box.
Answer:
2
Step-by-step explanation:
The average rate of change of a function over the interval a to b is:
(f(b) − f(a)) / (b − a)
In this case:
(f(4) − f(0)) / (4 − 0)
(7 − -1) / 4
2
Maya needs 54 cubic feet of soil for her garden. She already has 4.5 cubic feet of soil. Each bag contains 1.5 cubic feet of soil. How many bags of soil should maya purchase
Answer:
Maya needs 33 bags
Step-by-step explanation:
Let's call x the number of bags of soil. If each bag contains 1.5 cubic feet, then "x" bags do not contain a volume of:
1.5x.
As a volume of 4.5 cubic feet has been published.
[tex]y = 4.5 + 1.5x[/tex]
We need 54 cubic feet.
Then [tex]y = 54[/tex]
[tex]54 =4.5 + 1.5x[/tex]
Now we must solve the equation for x.
[tex]1.5x = 54 -4.5[/tex]
[tex]1.5x = 49.5[/tex]
[tex]x =\frac{49.5}{1.5}\\\\x=33\ bags[/tex]
an energy bar contains 9000 milligrams of protein. how much protein does it contain in grams
Answer:
9 Grams
Step-by-step explanation:
You would move the decimal over 3 times to the left from the end of 9000
To convert milligrams to grams, you should know that 1 gram is equal to 1000 milligrams. This is because "milli" in milligrams means one-thousandth of a gram.
If an energy bar contains 9000 milligrams of protein, to convert this amount to grams, you divide the milligrams by 1000 (because 1000 milligrams equals 1 gram).
Here's the calculation:
\( 9000 \text{ milligrams} \div 1000 = 9 \text{ grams} \)
So, an energy bar that contains 9000 milligrams of protein has 9 grams of protein.
emily's living room window is 2 5/6 feet wide the window in her bedroom is 1 1/3 feet wide how much wider is the living room window then her
Answer:
1 1/2 feet
Step-by-step explanation:
Living Room Window: 2 5/6 feet wide
Bedroom Window: 1 1/3 feet wide
2 5/6 - 1 1/3 = 2 5/6 - 1 2/6 = 1 3/6 = 1 1/2
The width of the window of the living room is 2.125 times the width of the window of the bedroom.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Emily's living room window is 2 ⁵/₆ feet wide the window in her bedroom is 1 ¹/₃ foot wide.
Convert the mixed fraction into a fraction number, then we have
2 ⁵/₆ = 17 / 6
1 ¹/₃ = 4 / 3
The ratio of the width of the window of the living room to the window of the bedroom is calculated as,
⇒ (17/6) / (4/3)
⇒ (17/6) x (3/4)
⇒ 17/8
⇒ 2.125
The width of the window of the living room is 2.125 times the width of the window of the bedroom.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
Vince has $500 which he puts into an investment that has a yearly growth rate of 8%.
Which statement best describes the function that could be used to model the value of Vince's investment, V(t), as a function of time in years?
Answer:
multiplication
Step-by-step explanation:
The investment as a function of time will be 500 + ((8 * t)/100)*500 where 't' represents the number of years.
What is percentage?Percentage is defined as a given part or amount in every hundred
Initial investment by Vince = $500
Increase percentage every year = 8%
Investment value after 1 year will be = 500 + ((8 * 1)/100)*500
Investment value after 2nd year will be = 500 + ((8 * 2)/100)*500
Continuing the pattern:
So, investment value after 't' years will be = 500 + ((8 * t)/100)*500
Learn more about percentages on:
https://brainly.com/question/24304697
#SPJ2
Determine if each set of ordered pairs represents a function.
Answer: Choices 1, 3, and 5 are functions
Step-by-step explanation:
To be a function, the x value can only be used once. In choices 2 and 4, the x value is repeated; therefore they are not functions.
Answer:
Step-by-step explanation:
Nine people were asked, "How many times have you been on an airplane?" Their responses are listed below 9, 3, 9, 8, 3, 3, 5, 3, 3
Answer:
The mean is 5 times
range - 6
mode - 3
median - 3
Step-by-step explanation:
to work out the mean you add 9+3+9+8+3+3+5+3+3 together which gives you 46 and then divide the answer by the total number of people which is 9 and the answer is 5.1 but you round it to 5
The net of a triangular prism is shown below what is the surface area of the prism !!!!! Help iTS DUe TOMORROW !!!!!!!
Answer: B.152
Step-by-step explanation:
5 * 8 = 40 * 2 = 80
6 * 8 = 48
4 * 6/2 = 12 * 2 = 24
80 + 48 + 24 = 152
The surface area of a triangular prism is determined by summing the areas of the five faces, which include two triangles and three rectangles. In the given example, the surface area totalled to 48 square cm.
Explanation:The surface area of a triangular prism can be found by summing the areas of all the faces. In the case of a triangular prism, there are two triangular faces and three rectangular ones. To find the area of a rectangle, you multiply the length by the width. For the triangle, you use the formula 1/2(base x height).
Let's assume as an example that we have a prism where each rectangle has dimensions of 3 cm by 4 cm, and the triangles have a base of 3 cm and height of 4 cm.
Calculating for the rectangular faces: 3 rectangular faces x area of rectangle (3 cm x 4 cm) = 3 x 12 square cm = 36 square cm.
Calculating for the triangular faces: 2 triangular faces x area of triangle (1/2 x 3 cm base x 4 cm height) = 2 x 6 square cm = 12 square cm.
Adding all together, the total surface area is 48 square cm.
Learn more about Surface Area of Prism here:https://brainly.com/question/32020716
#SPJ11
What is 2 1/6 ft= to inches as a mixed number?
Answer: 26
Step-by-step explanation:
because...
Feet result: 0.18055555556 ft.
Calculation: 2.1666666666666665" / 12
= 0.18055555556ft
But at the end your answer is going to 26.
So 2.1666666666666665 = 26
* Hopefully this helps:)
* Mark me the brainliest:)!!
Answer:
Step-by-step explanation:
2 1/6 ft = 24 inches plus (1/6)(12 in), or 24 inches plus 2 inches, or 26 inches.
2 1/6 is ALREADY a mixed number, in feet.
What missing angle of the figure
Answer:
138
Step-by-step explanation:
152+125=277
277-135=142
around 138
What number is equivalent to |−27| ?
Question 3 options:
a 27
-b 27
c 127
d − 127
Answer:
27
Step-by-step explanation:
Using the process of elimination and since their is no -27, 27 must be the answer
The little bars on each side of the number -27 represent absolute value. This means that you must take the positive of the number inside the absolute value. In this case the positive of -27 is...
A. 27
Hope this helped!
I love Shawn Mendes. I'll marry him one day. You'll see
if you invested $45,000 for 8 months at an interest rate of 2.75 % how much interest would you earn?
Answer:
You'd earn $825 in interest.
Step-by-step explanation:
The appropriate formula for simple interest is i = p·r·t, where p is the principal, r is the interest rate as a decimal fraction, and t is the time in years. Because 8 months constitutes 2/3 year, we have:
i = $45,000·(0.0275)(2/3) = $825.
You'd earn $825 in interest.
evaluate 3|-4|
12
4
-12
Answer:
12
Step-by-step explanation:
Absolute value means take the positive value of
3 |-4|
3 * 4
12
A 6-meter pole is supported by guy wires that are anchored to the ground as shown. What is sin D?
Answer:
0.8941
Step-by-step explanation:
sin D = opp / hyp = 6 m / 6.71 m = 0.8941
Answer:
sin D = 0.8942
Step-by-step explanation:
In the given Δ BCD.
sin D = [tex]\frac{\text{Length of pole}}{\text{Length of guy wires}}[/tex] = [tex]\frac{CA}{CD}[/tex] = [tex]\frac{Height}{Hypotenuse}[/tex]
= [tex]\frac{6}{6.71}[/tex]
Sin D = 0.8942
Therefore, Answer is sin D = 0.8942
identify the relative maximum value of g(x) for the function shown below
g(x) = 2/ x^2 +3
Answer:
The relative maximum value is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The given function is
[tex]g(x)=\frac{2}{x^2+3}[/tex]
We differentiate to obtain;
[tex]g'(x)=-\frac{4x}{(x^2+3)^2}[/tex]
At turning points [tex]g'(x)=-\frac{4x}{(x^2+3)^2}=0[/tex]
[tex]\implies x=0[/tex]
[tex]g''(x)=\frac{16x^2}{(x^2+3)^3}- \frac{4}{(x^2+3)^2}[/tex]
We apply the second derivative test to obtain:
[tex]g''(0)=\frac{16(0)^2}{((0)^2+3)^3}- \frac{4}{((0)^2+3)^2}=-\frac{4}{9}[/tex]
Since the second derivative is negative, there is a relative maximum at x=0.
We substitute x=0 into the original function to obtain the relative maximum value.
[tex]g(0)=\frac{2}{(0)^2+3}=\frac{2}{3}[/tex]
To find the relative maximum value of g(x) = 2/(x² + 3), one should evaluate the function at x = 0, giving the relative maximum value as 2/3.
The question is asking to identify the relative maximum value of the function g(x) = 2/(x² + 3).
To find the relative maximum, we need to find the critical points by taking the derivative of g(x) and setting it to zero. However, this function does not have a simple expression where the derivative is zero.
Instead, we note that because the denominator x² + 3 is always positive and has a minimum when x = 0, the function g(x) will have a maximum value when x = 0.
Thus, the relative maximum value of g(x) is obtained by plugging x = 0 into the function: g(0) = 2/(0² + 3) = 2/3.
ANSWER ASAP! 25 POINTS! WILL GIVE BRAINLIEST!
Rewrite the expression in the form k * x^n (k times x to the n power)
(4x)^2
Answer:
[tex]16(x^{2})[/tex]
Step-by-step explanation:
we know that
[tex](4x)^{2} =(4^{2})(x^{2})=16(x^{2})[/tex]
therefore
The expression in the form [tex]k(x^{n})[/tex] is equal to
[tex]k(x^{n})=16(x^{2})[/tex]
where
k=16
n=2
I also need help with this one, simplifying this radical expression. This ones weird.
Answer:
1
Step-by-step explanation:
Factorise numerators/ denominators where possible
3x² - 4x + 1 = (x - 1)(3x - 1)
x² - 1 ← is a difference of squares and factors as
x² - 1 = (x - 1)(x + 1)
Expressing the product in factored form
[tex]\frac{(x-1)(3x-1)}{(x-1)(x+1)}[/tex] × [tex]\frac{x+1}{3x-1}[/tex]
Cancel common factors on numerator/denominator, that is
Cancel (x - 1) , (x + 1) and (3x - 1), leaving the simplified form 1
Answer: 1
Step-by-step explanation:
2r - 12 = 12 - 10r whats the answer
Answer:
r=2
Step-by-step explanation:
bring the numbers to the other sides
Answer:
dude what is r?
Step-by-step explanation:
for example
3 + 3z - 10
if z is 2
3 + 3 × 2 - 10
What is the measure of ZRST?
А. 188°
B. 47
C. 86
D. 94
Answer:
B
Step-by-step explanation:
The measure of the angle on the circle formed by the chords RS and TS is half the measure of the arc RT intersected by the 2 chords,
∠RST = 0.5 × 94° = 47° → B
Answer: 47
Step-by-step explanation:
In the triangle below, which equation can be used to solve for x?
a)x=13sin50/sin75
b)x=13sin75/sin50
c)13sin55/sin75
d)13sin75/sin55
Answer:
d)13sin75/sin55
Step-by-step explanation:
1)Given
inΔVWU, ∠V= 75°
∠U= 50°
Finding ∠W:
∠W= 180-(75+50)
=180-(125)
= 55
Now finding x, using law of sine
x/sinV = 13/sinW
Putting the values in above we get:
x/sin75=13/sin55
Re-arranging, we get:
x= 13sin75/sin55 !