Answer:
[tex]6^2=36[/tex]
Step-by-step explanation:
[tex]10^2-4^3=100-64=36=6^2[/tex]
What is the simplified form of the expression the quantity x squared minus 4x minus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?
The simplified form of the given expression [tex]\frac{x^2-4x-21}{4(x+3)}[/tex] is [tex]\frac{x-7}{4}[/tex].
How to simplify a fractional expression?The steps to simplify a fractional expression are:
Factorize the expressions both in the numerator and the denominator using different methodsRemove the common terms in the numerator and denominatorThus, the simplified expression will be obtained.Calculation:The given expression is [tex]\frac{x^2-4x-21}{4(x+3)}[/tex]
Factorizing the numerator:
x² - 4x - 21 = x² - 7x + 3x - 21
= x(x - 7) + 3(x - 7)
= (x - 7)(x + 3)
Then,
[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{(x-7)(x+3)}{4(x+3)}[/tex]
common factor (x + 3) is canceled out from both the numerator and the denominator
So,
[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{x-7}{4}[/tex]
Therefore, the simplified expression is [tex]\frac{x-7}{4}[/tex].
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Answer:x-3/4
Step-by-step explanation:
(x-3)(x+7)/4(x+7)
=x-3/4
if x = 2z and y = 3z, find z
Answer:36
Step-by-step explanation:
Let name the missing angle in the triangle w.
We know that x+z+w=180
We also know that z+w=3z=y.
That means that w=2z.
x=2z, so, 2z+2z+z=180
z=36
Answer:
Z=36 degrees
Step-by-step explanation:
Since angles x and y are supplementary, you know that they add up to 180 degrees.
Since we know that:
=x+y
=2z+3z
=5z
=180 degrees
180/5=36 degrees, so Z=36 degrees
Find each of the following:
pls help me ASAP!!
Step-by-step explanation:
try this option, answer is marked with red colour.
solve it please as soon as possible with step by step explanation
By definition of real field and algebra properties we conclude that the product of three positive integers is always equal to a positive integer.
How to make a conjecture
First, we state the conjecture: The product of three positive integers equals a positive integer. Second, we prove if the conjecture is true:
Integers are part of the real field, which mean that the product of two integers is also an element of that field. By algebra we know that the product of two positive integers is equal to another positive integer. Thus, the product of three positive integers is always equal to a positive integer.
Here is an example:
2 × 5 × 7
10 × 7
70
In a nutshell, the conjecture has been proved true.
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what is the measure of XYZ?
46°
94°
a. 46°
b. 140°
c. 94°
d. 70°
Answer:
46+96=140°_÷__^_^^^^=^
Given f (x) = 4x + 3 – 2, what is f –1(x)?
f –1(x) = log4(x – 3) + 2
f –1(x) = log4(x + 3) – 2
f –1(x) = log4(x – 2) + 3
f –1(x) = log4(x + 2) – 3
The inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3
How to determine the inverse function?The function is given as:
f(x) = 4^(x + 3) -2
Rewrite as:
y = 4^(x + 3) -2
Swap x and y
x = 4^(y + 3) -2
Add 2 to both sides
x + 2 = 4^(y + 3) -2 + 2
This gives
x + 2 = 4^(y + 3)
Take the logarithm of both sides
log(x + 2)= log(4)^(y + 3)
Apply the base rule of logarithm
log(x + 2)= (y + 3)log(4)
Divide both sides by log(4)
log(x + 2)/log(4) = y + 3
Apply the change of base rule of logarithm
log₄(x + 2) = y + 3
Subtract 3 from both sides
log₄(x + 2) - 3 = y + 3 - 3
Evaluate the difference
log₄(x + 2) - 3 = y
Rewrite as:
y = log₄(x + 2) - 3
Rewrite as:
f-1(x) = log₄(x + 2) - 3
Hence, the inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3
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Identify the coordinates of the vertices after the transformation
Answer:
A' is (-2,-1)
B' is (3,0)
C' is (2,4)
Step-by-step explanation:
A rain gutter is to be made of aluminum sheets that are 16 inches wide by turning up the edges 90. See the illustration.
(a) What depth will provide maximum cross-sectional area and hence allow the most water to flow?
(b) What depths will allow at least 30 square inches of water to flow?
Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.
How much can the maximum cross-sectional area?Assuming that the depth is x, the area would be:
= x (16 - 2x)
= 16x - 2x²
The maximum of the parabola is:
x = -b / 2a
= - 16 / (2 x -2)
= -16 / -4
= 4 inches
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Alex, Barry, Charles, David, and Eric paint houses for a living. Alone, Alex can paint an entire house in 24 hours, Barry in 26 hours, Charles in 20 hours, David in 21 hours and Eric in 27 hours. If they work together, approximately how long will it take them to paint 3 houses, rounded to the nearest hour?
It would take 14 hours for all of them to paint the three houses.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let t represent the time it would take them working together, hence:
(1/24 + 1/26 + 1/20 + 1/21 + 1/27)t = 3
t = 14 hours
It would take 14 hours for all of them to paint the three houses.
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What is 681x239 please help
681×239 = 162,759
..... ......
162,759 is answer
happy to help
What is the standard form equation of an ellipse that has vertices (−2,14) and (−2,−12) and co-vertices (9,1) and (−13,1)?
Answer:
[tex]\frac{(x+2)^2}{121} + \frac{(y-1)^2}{169} = 1[/tex]
Step-by-step explanation:
First, we identify that the vertices are vertical.
(an image below is attached if you want to see a visualization)
Therefore, the equation is such:
[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]
(h,k) is the center of the ellipse, which we could easily calculate by finding the midpoint between any pair of vertices.
This gets us (-2, 1)
Therefore, h = -2, k = 1
Now we want to find a,
we know the length of the major axis is 2a, and in this case, our length of the major axis is 26. So a = 13
Now we want to find b,
We know the length of the minor axis is 2b, and in this case, our length is 22, so b = 11
Now we will just plug in all the values and simplify to get our answer! B)
solve the inequaility - x/4 <2
❄ Hi there,
let us start by considering this: What should we do to get x all by itself?
Since it's
divided by 4multiplied by -1we should
multiply (both sides) by 4divide (both sides) by -1So, let's start.
[tex]\sf{\dfrac{-x}{4}\times4 < 2\times4}}[/tex]
[tex]\sf{-x < -8}[/tex]
[tex]\sf{x > 8}[/tex]
When we divide both sides of an inequality by a negative number, we do "the inequality flip" and flip the inequality sign.
❄
Does this graph show a function? Explain how you know. O A. No, the graph fails the vertical line test. OB. No; there are y-values that have more than one xvalue. OC. Yes; the graph passes the vertical line test. OD. Yes; there are no y-values that have more than one x-value.
The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.
What is a function in the graph?The collection of all points in the plane with the form (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.Use the vertical line test to establish if a graph reflects a function. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line crosses it at more than one location.First-order variables are present in linear functions, and the graph's placement is determined by two constants. These operations graph into a line in every case. The slope of the line is determined by the constant m. The slope of the line will slope up if it is positive and down if it is negative.
The graph represents a parabola.
The graph can be a function if it passes the vertical line test.
The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.
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What is the measure of ABC in the figure below?
Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.
Hence, option D is the correct answer.
What is the measure of ABC in the figure below?Two angles are called complementary when their measures add to 90 degrees.
From the diagram; Angle ABD and Angle DBC are complementary angles that add up to make 90 degrees.
Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.
Hence, option D is the correct answer.
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Curves defined using parametric equations have an orientation
true or false?
Answer:
True
Step-by-step explanation:
So this problem is asking whether Parametric because have an orientation and the short answer to that is that this is true. Parametric curves do have an orientation and we'll just do a little demonstration to share. Why? So let's take these very standard privatization of the unit circle where X is he going to cause of tea and why is equal to sign of tea now? The final part of defining the characterization is defining that the main range of tea on will take t to go from zero to two pi Andi, In this case, this is the this parts of circle going in this direction in the counter clockwise direction. And this is because as X as he goes from zero to play over two x decreases and signed increases on it sets us off on this direction as if that's one orientation off this curve of the circle. But we can alter this curve to get a different orientation. So if we were to take the Parametric equation given by X is equal to the co sign a minus T and why is equal to the sign of minus T in this case? Well again, take the domain to be from 0 to 2 pi. But because of the mind, the sign when it the mind sign doesn't actually affect X, it doesn't effect for co sign Well, it does affect the sign of minus T. So as T increases, the X value still decreases. But the Y value initially decreases as well, so this sets the arrows off on the clockwise direction. So this is another orientation off the same curve. So we've got two very different characterizations that describe the same physical curve. But because of the differences, the curve is constructed in opposite direction, and that is what the orientation defines. So it's very important to make sure that when you're drawing and describing the curve, you're parametric equations are in the correct orientation because otherwise you may encounter some difficulties later on. Because you'll be working with equation start that are, in fact, wrong
Thank you,
Eddie.
Three quarters of a cake was eaten at a party .how much cake is left?
Hi! ◈
Answer:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1/4 of the cake was left
Step-by-step explanation:
Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4
[tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]
_____________________
[tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]
Hope this made sense to you !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CalligrxphyIn London today, twice the high temperature was more than five times the high temperature minus eighty-seven. In interval form, what are the possible temperatures?
The possible temperatures are represented by (-∝, 29)
How to determine the possible temperatures?Let the high temperature be x
So, the statement can be represented as:
2x > 5x - 87
Subtract 5x from both sides
-3x > -87
Divide both sides by -3
x < 29
In interval form, we have (-∝, 29)
Hence, the possible temperatures are represented by (-∝, 29)
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a right triangle has side lengths of 6, 10, and x. find x if it is the hypotenuse
X= root 6^2 + 10^2
X=2 root 34
So, x is 11.66 to 2d.p
(root means square root)
Hope this helps!
Answer:
x = 11.66
Step-by-step explanation:
Hello!
We can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
a = legb = legc = hypotenusePlug the values of 6 and 10 into the formula to solve.
Find the Hypotenuse[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 10^2 = c^2[/tex][tex]36 +100 = c^2[/tex][tex]136 = c^2[/tex][tex]c = \sqrt{136[/tex][tex]c \approx 11.66[/tex]The hypotenuse is approximately 11.66.
A certain radioactive material decays in such a way that the mass in kilograms remaining after t years is given by the function
m(t)=120e−0.018t
How much mass remains after 50 years?
The mass of radioactive material remaining after 50 years would be 48.79 kilograms
How to determine the amountIt is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.
Given the radioactive decay formula as
m(t)=120e−0.018t
Where
t= 50 years
m(t) is the remaining amount
Substitute the value of t
[tex]m(t) = 120e^-^0^.^0^1^8^(^5^0^)[/tex]
[tex]m(t) = 120e^-^0^.^9[/tex]
Find the exponential value
m(t) = 48.788399
m(t) = 48.79 kilograms to 2 decimal places
Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms
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A conduit of circular cross section has 7 cables all same diameter. Inside diameter of conduit is 30cm. What is the cross sectional area of the conduit not part of the 7 cables
The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²
What is the cross sectional area of the conduit not part of the 7 cables?It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.
Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;
where radius, r = D/2 = 30/2.
Area = πr² = 3.14 × (30/2)² = 706.5cm²
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binary add:
(e) 10110₂ +1010₂ = (?)
Answer:
278,861,394
Step-by-step explanation:
put in the calculator e but then just square the numbers add it and there is your answer
15. Solve the following inequality: 38 < 4x + 3 + 7 - 3x.
OA.x < 4
OB.x>4
O C. x < 28
OD. x > 28
Step-by-step explanation:
38<4x+3+7-3x
4x+3+7>38
4x+3+7<3x
X>7
X<-10
= Ø
Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB
The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.
Which inequality explains why the three segments cannot be used to construct a triangle?Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.
Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.
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Number 8 is the answer 90*
Answer:
E
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
Consider the triangle on the left
3rd angle = 180° - 60° - 90° = 180° - 150° = 30°
the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so
∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°
For f(x) = 3x+1 and g(x) = x2 - 6, find (F/g)
Answer: [tex]\frac{3x+1}{x^{2}-6}[/tex]
Step-by-step explanation:
(f/g) represents the division of function f by function g.
Find the area of the region enclosed by the curves yequals
xsquaredminus2x
and yequals
minusxsquaredplus2
x.
The area enclosed by the given 2 curves is; 8/3 or 2.67
How to Solve Integration with Limits?We want to find the area enclosed by the curves;
y = x² - 2x
y = -x² + 2x
The point of intersection of the parabola and the line is given by;
x² - 2x = -x² + 2x
2x² - 4x = 0
Solving this gives;
x = 0, 2
Therefore, the area bounded by the parabola and the line between x = 0 and x = 2 is given as;
A = ∫₀² (-x² + 2x - x² + 2x)
A = ∫₀² (-2x² + 4x)
Using online integration calculator here gives;
A = 2.67
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help me please
What is the midpoint of the horizontal line segment graphed below?
A. (4,3)
B. (8,6)
C. (8,3)
D. (4, 6)
-10
10
(-2,3)
$10
(10, 3)
10
Answer: A
Step-by-step explanation:
A summer camp needed
1,148 popsicles. Boxes of
popsicles were sold with
8 in each. How many
boxes did they have to
buy to have enough
popsicles? How many
were left over?
Answer:
144 boxes, 4 popsicles left over
Step-by-step explanation:
# of boxes and the remainder: 1148/8 = 143 boxes 4 popsicles left over
Since they need to buy full boxes we add 1 to 143 = 144 boxes
A full box is 8 and they only need 4 more so they have 4 left over.
2. Merchandise from the vendor carries an invoice of July 1 and is received on July 4. Terms are 2/10 net 30 EOM, and the invoice is for $5,000. What amount should be remitted if the retailer pays the bill on July 13?
The retailer would remit $4,900 to the vendor on July 13.
What is invoice date?
The invoice date is the date written on this which is the same as the date the goods were shipped to customer, in this case, invoice date is July 1.
Invoice receipt date?
This is the date the customer received the invoice as well as the goods sent by the vendor, which is July 4 in this case.
2/10 means that a discount of 2% is available if the customer pays within the first 10 days, which starts counting from July 4, not July 1, because the customer actually received the invoice on July 4.
From July 4 to July 13 is a period of 10 days, which means that the 2% cash discount that customer would be entitled if payment is made within the first 10 days is still available
discount=2%*$5000
discount=$100
The retailer would remit the invoice price of $5,000 minus the discount.
amount remitted=$5000-$100
amount remitted=$4,900
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I can't find the answer for 46.3 divided by 1.5 Help!
The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex] the result of the division is [tex]30.8666667[/tex] in decimal form.
When a large number is distributed into small numbers of equal parts is called division.
The number [tex]1.5[/tex] is not a factor of [tex]46.3[/tex] , on dividing them the remainder is not zero.
Therefore, first convert [tex]1.5[/tex] it into a whole number by multiplying it [tex]10[/tex] so it becomes [tex]15[/tex] .
Then convert [tex]46.3[/tex] it into a whole number by multiplying it by [tex]10[/tex] so it becomes [tex]463[/tex]
Here, [tex]\dfrac{463 \times 10}{15 \times 10}[/tex] which results in [tex]\dfrac{463}{15}[/tex].
Now, divide [tex]\dfrac{463}{15}[/tex] , the result will be [tex]30.8666667[/tex].
The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex] the result is [tex]30.8666667[/tex].
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