Answer:
Step-by-step explanation:
"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false as it now stands.
If we combine -3x^2 and 3x^2, we get 0, so:
"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is equivalent to
"The sum of (expression) and 7x^2 is 10x^2".
Subtracting 7x^2 from both sides yields (expression) = 3x^2.
So: Although "The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false,
"The sum of 3x^2 and 7x^2 is 10x^2" is true, and the formerly missing term is 3x^2.
How do I add -6 and positive 13
Answer:
7
Step-by-step explanation:
This operation is identical to subtracting 6 from 13. The correct result is 7.
The endpoints of a diameter of a circle are A(2,1) and B(5,5). Find the area of the circle in terms of pi.
Answer:
The area of the circle is [tex]A=6.25\pi\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the diameter of circle
we know that
The diameter of the circle is equal to the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]AB=\sqrt{(5-1)^{2}+(5-2)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
therefore
the diameter of the circle is
[tex]D=5\ units[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
[tex]r=5/2=2.5\ units[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (2.5)^{2}[/tex]
[tex]A=6.25\pi\ units^{2}[/tex]
Write and equation in point-slope form for the line through the given point with the given slope
(10,-9); m=-2
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = - 2 and (a, b) = (10, - 9), hence
y - (- 9) = - 2(x - 10), that is
y + 9 = - 2(x - 10) ← in point- slope form
Answer: [tex]y+9=-2(x-10)[/tex]
Step-by-step explanation:
We know that the equation of a line in point slope form passing through point (a,b) and having slope 'm' is given by :-
[tex](y-b)=m(x-a)[/tex]
Given : Point : (10,-9)
Slope : m=-2
Then , the equation of a line in point slope form passing through point (10,-9) and having slope '-2' is given by :-
[tex](y-(-9))=-2(x-10)\\\\\Rightarrow\ y+9=-2(x-10)[/tex]
Which expression is a difference of cubes?
Answer:
Option 4 is correct.
Step-by-step explanation:
Given the following options
we have to choose the difference of cubes.
Option 1:
[tex]9w^{33}-y^{12}[/tex]
[tex]9(w^{11})^{3}-(y^4)^3[/tex]
which is not the difference of cubes
Option 2:
[tex]18p^{15}-q^{21}[/tex]
[tex]18(p^5)^3-(q^7)^3[/tex]
which is not the difference of cubes
Option 3:
[tex]36a^{22}-b^{16}[/tex]
[tex](6a^{11})^2-(b^8)^2[/tex]
which is the difference of square
Option 4:
[tex]64c^{15}-a^{27}[/tex]
[tex](4c^5)^3-(a^9)^3[/tex]
which is the difference of cubes.
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
A - (–2, 0) and (2, 5)
B - (–4, 5) and (4, –5)
C - (–3, 4) and (2, 0)
D - (1, –1) and (6, –5)
E - (2, –1) and (10, 9)
Answer:
A and E
Step-by-step explanation:
A line has a slope of -4/5, then a perpendicular line has a slope 5/4, because
[tex]-\dfrac{4}{5}\cdot \dfrac{5}{4}=-1[/tex]
Find the slopes of the lines in all options:
A. True
[tex]\dfrac{5-0}{2-(-2)}=\dfrac{5}{4}[/tex]
B. False
[tex]\dfrac{-5-5}{4-(-4)}=-\dfrac{5}{4}[/tex]
C. False
[tex]\dfrac{0-4}{2-(-3)}=-\dfrac{4}{5}[/tex]
D. False
[tex]\dfrac{-5-(-1)}{6-1}=-\dfrac{4}{5}[/tex]
E. True
[tex]\dfrac{9-(-1)}{10-2}=\dfrac{5}{4}[/tex]
Answer:
C
Step-by-step explanation:
=(0-4)/(2+3)
=-4/5
What is a requirement of adjacent angles?
Adjacent angles must be vertical.
Adjacent angles must be supplementary.
Adjacent angles must share a vertex.
Adjacent angles must share interior points.
Answer:
Adjacent angles must share a vertex.
Step-by-step explanation:
we know that
Two angles are Adjacent when they have a common side and a common vertex
therefore
Adjacent angles must share a vertex.
Answer:
Adjacent angles must share a vertex.
Im so sorry I am so late on answering this question....
Hope the answer (my answer) helps!
HELP Geometry, can someone please answer this
Check the picture below.
Annabelle's total pay varies directly with the number of hours she works. If she works 4 hours, she earns $100. How much does Annabelle earn if she works 6 hours? Plz show work:)
A.$90.
B. $120.
C. $150.
D. $300
Answer:
C. $150 :)
Step-by-step explanation:
If Annabell works 4 hours and earns $100 that means for every hour she earns $25 so 25×4=100 so then multiply 25×6=15]
Answer: C. $150.
Step-by-step explanation:
When two quantities x and y are directly proportional ,then the equation of direct proportion is given by :-
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Given : Annabelle's total pay varies directly with the number of hours she works. If she works 4 hours, she earns $100.
Let [tex]x_1=100\ ;\ y_1=4 \ :\ x_2=x,\ y_2=6[/tex], then we ahve
[tex]\dfrac{100}{4}=\dfrac{x}{6}\\\\\Rightarrow\ x=\dfrac{100\times6}{4}=150[/tex]
Hence, Annabelle earns $150 if she works 6 hours.
which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4) select all that apply
Answer:
the answers are A B AND D
Step-by-step explanation:
To find perpendicular lines you take the slope and change the sign and find the reciprocal. after doing that you set it up as a new equation that you will use to find b using the point.
in this case
y= - 2/5x +b
plug in the x and y values of the point (5, -4) to find b
b= -2
you put that together to get the equation
The equation of the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4) is y = -0.4x - 2.
Explanation:The given equation is 5x - 2y = -6. First step is to convert this to the slope-intercept form (y = mx + b) to find the slope. To do this, solve for y in terms of x, which looks like y = 2.5x + 3. The perpendicular line would have a slope that is the negative reciprocal this slope (m = -1/2.5 or -0.4).
Next, apply the point-slope formula (y - y1 = m(x - x1)) where m is the slope and (x1, y1) is the point that the line passes through. In this case, (x1, y1) is (5, -4), and slope m is -0.4. Then, y - (-4) = -0.4(x - 5), results to y + 4 = -0.4x + 2, finally gives y = -0.4x - 2 as the equation of the line that is perpendicular to 5x - 2y = -6 and passes through the point (5, -4).
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Given that the circles are congruent, can you conclude that ∠jkn is ≅ ∠gfh
Answer:
Yes
Step-by-step explanation:
Think simple.
The picture has already provided us with the information that ∠EFT ≅ ∠LKM, and we also have:
∠EFT ≅ ∠GFH (opposite angles)
∠LKM ≅ ∠JKN (opposite angles as well)
Therefore ∠JKN ≅ ∠GFH
Factor the expression below.
x^2 – 6x + 9
A.
(x - 3)(x - 3)
B.
3(x2 - 2x + 3)
C.
(x - 3)(x + 3)
D. (x + 3)(x + 3)
Answer:
A.
(x - 3)(x - 3)
Step-by-step explanation:
x^2 – 6x + 9
What 2 numbers multiply to 9 and add to -6
-3*-3 =9
-3+-3 = -6
(x-3) (x-3)
What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?
Answer:
rotate 180 degrees ccw from (0,0)
Answer:
We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.
Step-by-step explanation:
We are given a graph which Rectangle ABCD and A'B'C'D'
To find : Set of transformation
From the graph,
Vertex of the Rectangle ABCD,
A( -4 , 2 ) , B ( -4 , 1 ) , C ( -1 , 1 ) and D ( -1 , 2 )
Vertices of Rectangle A'B'C'D'
A( 4 , -2 ) , B ( 4 , -1 ) , C ( 1 , -1 ) and D ( 1 , -2 )
Clearly from above,
we get that coordinates of the vertices of Rectangle A'B'C'D' is negative of the coordinates of the vertices of Rectangle ABCD .
That is if Coordinates of A( x , y ) then A'( -x , -y )
This transformation is done when we rotate the given figure by 180° about origin.
Therefore, We get Rectangle A'B'C'D' by rotating the Rectangle ABCD by 180° about origin.
write two decimals that are equivalent to the given decimal
Answer:
2.2
2.20
Explanation
You can add zeros or take them away and the number will still have the same value.
Evaluate 4k2 + 3 when k = 5
Answer:
103
Step-by-step explanation:
Evaluate 4k2 + 3
To evaluate 4k² + 3, when k = 5, which means when you sees k, put 5 in replacement
4k² + 3 = 4(5)² + 3
4(5×5) + 3
4(25) + 3
open the bracket
4 × 25 = 100
∴ 100 + 3 = 103
Please mark me brainliest
[tex]\text{Hey there!}[/tex]
[tex]\text{If k = 5 the replace the 'k' value with 5}[/tex]
[tex]\text{4(5)}^2+3[/tex]
[tex]\text{(5)}^2=5\times5=25[/tex]
[tex]\text{4 (25)+ 3 = ?}[/tex]
[tex]\text{4 (25) = 25 + 25 + 25 + 25 = 100}[/tex]
[tex]\text{100 + 3 = 103}[/tex]
[tex]\boxed{\boxed{\bf{Your\ answer: 103}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why DEF= KLM?
Check all that apply.
The congruence theorems that will be used to prove that both triangles are congruent are: C. LL E. SAS.
What is the LL Theorem?The LL theorem is a triangle congruence theorem that states that if the two pairs of legs of two right triangles are congruent, then the triangles are congruent.
What is the SAS Theorem?The SAS theorem is a triangle congruence theorem that states that if the two pairs of sides and a pair of included angles of two triangles are congruent, then the triangles are congruent.
Based on the information given, the theorem that can be used to show both triangles are congruent are: C. LL E. SAS
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Triangle DEF can be proven congruent to triangle KLM using the Leg-Leg (LL) Theorem, Side-Angle-Side (SAS) Theorem, and Hypotenuse-Leg (HL) criterion .
The correct answer is option B, C and E.
In geometry, a congruence theorem is a statement that two geometric figures are congruent, meaning that they have the same size and shape. There are many different congruence theorems, but the most common ones are the Side-Angle-Side (SAS) Theorem, the Angle-Side-Angle (ASA) Theorem, and the Leg-Leg (LL) Theorem.
The LL Theorem is a special congruence theorem that applies to right triangles. It states that if two right triangles have two congruent legs, then the triangles are congruent. This means that all of their corresponding sides and angles are congruent.
In the diagram provided, we have two right triangles, DEF and KLM. We are given that DE = KL and DF = LM. Since these are the legs of the two triangles, we can use the LL Theorem to conclude that DEF = KLM.
Hypotenuse-Leg (HL): This criterion applies specifically to right-angled triangles. If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. Here, the right angles at D and K establish the triangles as right triangles, and the equal side lengths ED = KL and DF = KM complete the congruence conditions.
We cannot use the HL Theorem because the diagram does not explicitly show that the two triangles are right triangles.
Therefore, from the given options the correct one is B , C and E.
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If (a, –5) is a solution to the equation 3a = –2b – 7, what is a?
Question 11 options:
a)
-1
b)
4
c)
0
d)
1
Answer:
d) 1⃣
Step-by-step explanation:
Multiply -5 by -2 to get , then deduct 7 to get 3. So, you now know that 3 = 3a; 1 = a.
the area of a rectangular wall of a barn is 252 square ft. its length is 10 ft longer than twice its width. find the lenght and width of the barn
Answer:
L=9 ft
W=28 ft
Step-by-step explanation:
LW=252
L=10+2W
Plug 2nd into 1st
(10+2W)W=252
Distribute
10W+2W^2=252
Divide both sides by 2
5W + W^2=126
Reorder using commutative property
W^2+5W =126
Subtract 126 on both sides
W^2+5W-126=0
What are two numbers multiply to be -126 and add to be 5?
My scratch paper:
-126=-2(63)
-126=-2(7)(9)
-126=-14(9)
So 14(-9) is -126 and 14+(-9)=5 so these are our magic numbers
(W+14)(W-9)=0
W=-14 or W=9
So W=9 is what makes sense here sense length can't be negative
Now let's go back and find L...
L=10+2W=10+2(9)=10+18=28
The problem can be solved by setting up a quadratic equation based on the given information. By solving the equation, we find that the width is 7 feet, and the length is 24 feet.
Explanation:In this problem, we are given that the area (A) of the rectangular wall is 252 square feet, and the length (L) of the wall is 10 feet longer than twice its width (W). We need to find both the length and width of the barn. The formula for the area of a rectangle is A = L × W.
From the problem, we know that L = 2W + 10. Substituting this into the formula gives us A = W × (2W + 10). Set this equal to 252 to get 252 = W × (2W + 10). Solving this quadratic equation, we find that the width of the barn is 7 feet. Substituting this value into L = 2W + 10, the length of the barn is 24 feet.
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Which of the following points is not coplanar with points C, D and E?
it's r because it does not sit on the same plane as the rest of the points that are given.when looking at the diagram c,d and e are all connected to the square on the bottom of the pyramid. The same goes for points u,s and a. The point R is different by sitting on one of the triangles of the pyramid.
The point R is not coplanar with C, D, and E. This is because point R is not lying in the plane of C, D, and E.
What are coplanar points?The points which lie on the same plane are said to be coplanar points.
Verifying the given points:The given points are R, A, S, and U
The considered pane is w.r.t the points C, D, and E.
So, point A is forming a square with the points C, D, and E. So, it is coplanar with these points.
Point S is on the surface of the plane formed by ACDE. So, it is coplanar.
Point U is also in the plane w.r.t point C, D, and E. So, it is a coplanar point.
But point R does not lie in the plane w.r.t C, D, and E. So, it is not coplanar with points C, D, and E.
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fine the value of 9-[4^2-(3+2)]
[tex]9-(4^2-(3+20)=9-(16-23)=9-(-7)=16[/tex]
What is the value of x?
a)20
b)35
c)60
d)70
Answer:
x is equal to 20, or the answer A
Step-by-step explanation:
They are opposite angles so they are equal to each other. When you set up the equation (x+40)=3x, you get the answer to be 20. hope this helped!
For this case we have to define by opposite angles the vertex that:
[tex]x + 40 = 3x[/tex]
Subtracting 3x on both sides of the equation:
[tex]x-3x + 40 = 0\\-2x + 40 = 0[/tex]
Subtracting 40 from both sides of the equation:
[tex]-2x = -40[/tex]
Dividing between -2 on both sides of the equation:
[tex]x = \frac {-40} {- 2}\\x = 20[/tex]
So, we have that [tex]x = 20[/tex]
ANswer:
[tex]x = 20[/tex]
Choose the equation that represents a line that passes through points (-1,2) and (3,1)
A. 4x-y=6
B.x+4y=7
C. x-4y =-9
D.4x+y=2
Answer:
B. x + 4y = 7Step-by-step explanation:
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\============================[/tex]
[tex]\text{We have the points:}\ (-1,\ 2)\ \text{and}\ (3,1).\\\\\text{Substitute:}\\\\m=\dfrac{1-2}{3-(-1)}=\dfrac{-1}{4}=-\dfrac{1}{4}\\\\y-2=-\dfrac{1}{4}(x-(-1))\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{convert to the standard form}\ Ax+By=C\\\\y-2=-\dfrac{1}{4}(x+1)\qquad\text{multiply both sides by 4}\\\\4y-8=-(x+1)\\\\4y-8=-x-1\qquad\text{add 8 to both sides}\\\\4y=-x+7\qquad\text{add x to both sides}\\\\x+4y=7[/tex]
The equation of a line passing through points (-1, 2) and (3, 1) can be determined using the slope formula, which is (y2 - y1)/(x2 - x1). The resulting slope is -1/4 or -0.25. Unfortunately, none of the provided options match this description.
Explanation:The subject of the question is about finding the equation of a line that passes through the points (-1,2) and (3,1). To find the correct equation, we need to use the formula for the slope of a line which is: (y2 - y1) / (x2 - x1). Plugging in the coordinates (-1,2) and (3,1) will give us a slope of -1/4 or -0.25. This slope should be the coefficient of 'x' in the correct equation. None of the provided choices A, B, C, D have a coefficient of -0.25 for x, therefore, unfortunately, none of these equations represent a line that passes through the points (-1,2) and (3,1).
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Danika signs up to work for 3 1/2 hours at the science fair. If each work shift is 3/4 hour, how many shifts will Danika work?
Show your work.
namely, how many times does 3/4 go into 3½? Let's firstly convert the mixed fraction to improper fraction.
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\div \cfrac{3}{4}\implies \cfrac{7}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]
Answer:
Danika signed up to work for 3.5 hours at the science fair, if each work shift is 3/4 hour = 0.75 hours, the amount of shifts will be:
Shifts = 3.5/0.75 = 4,66 ≈ 5 shifts. Given that shifts have to be an integer number, we need to round the result to the nearest integrer.
Therefore, Danika will work 5 shifts.
What is p(-2)?
Rounded to the nearest tenth please:)
Answer:
0.2
Step-by-step explanation:
[tex]\text{f(x) = }\dfrac{90}{9+\frac{50}{e^x}}[/tex]
[tex]\text{f(-2) = }\dfrac{90}{9+\frac{50}{e^{-2}}}[/tex]
[tex]\text{f(-2) =} \dfrac{ 90 }{9 + 50*e^2}[/tex]
Now we can work out the denominator separately.
9 + 50*e^2
9 + 50*7.389
9 + 369.45
378.45
Now use this number to get the final answer.
f(-2) = 90 / 378.45
f(-2) = 0.237 To the nearest tenth
f(-2) = 0.2
There was a lot of movement for that e^x factor make sure you study carefully how that moved around and why. It's a good question. Get what you can from it.
Find the discriminant of 5x^2+3x-5=0 for x
For this case we have that by definition, a quadratic equation is of the form:
[tex]ax ^ 2 + bx + c = 0[/tex]
Its roots are given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
By definition, the discriminant is given by:
[tex]D = b ^ 2-4 (a) (c)[/tex]
According to the given equation we have to:
[tex]a = 5\\b = 3\\c = -5[/tex]
Substituting:
[tex]D = 3 ^ 2-4 (5) (- 5)\\D = 9 + 100\\D = 109[/tex]
Answer:
The discriminant is 109
What is nine and two hundredths as a decimal?
Step-by-step explanation:
9.02
remember when dealing with decimals:
0.(tenth)(hundredths)(thousandths)
Nine and two hundredths as a decimal is 9.02.
Explanation:The question asks for the decimal representation of nine and two hundredths. In the decimal number system, 'and' corresponds to the decimal point. So, the answer to the question is 9.02. This is because the 'nine' is in the whole number part before the decimal point and 'two hundredths' is represented by '02' after the decimal point.
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Can someone answer C. Please it’s my last try I got it wrong 2 times so please explain!
Answer:
5.
Step-by-step explanation:
What you require is the area of the rectangle whose base is between 210 and 215.
The number having levels between 210 and 214
= 20 * the relative frequency
= 20 * 0.25
= 5 (answer).
The slope of the line whose equation is x-3y= 1 is
0-3
-1/3
0
0
1/3
x-3y= 1
The equation needs to be rewritten in proper Slope intercept form ( y = mx+b) where m is the slope and b is the y-intercept.
x-3y = 1
Subtract x from each side:
-3y = 1-x
Divide both sides by -3:
y = 1/-3 - x/-3
Simplify:
y = 1/3x - 1/3
The slope is 1/3
Serena bought 5 shirts for $6 each spent $7 on lunch. she paid for the shirts and lunch using her debit card. The change in the balance of serena’s checking account can be represented by the expression shown. 5(-6) + (-7) which integer represents the change in the balance of serena’s checking account from these purchases? A // -37. B // 23. C // -18. D // 4
Answer:
your answer is A// -37
Step-by-step explanation:
1 shirt=$6
5 shirts= 5 × $6
=$30
lunch= $7
So in total she spent:
$30 + $7= $37
And from what we are given above; the balance in her account is
5(-6) + (-7)
= -30 - 7= -37
If f(x) = 5x3 – 2 and g(x) = x+1, find (f - g)(x).
Answer:
10
Step-by-step explanation:
x=2
f(2)=5x3-2=15-2=13/2=6.5=f
g(2)=2+1=3/2=1.5=g
(6.5-1.5)(2)=(13-3)=10
Answer:
5x³ - x - 3
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 5x³ - 2 -(x + 1) = 5x³ - 2 - x - 1 = 5x³ - x - 3
r(x) = -0.21x^3 + x^2 - 8.1x - 3 for x= -1 and x = 2
Answer:
r(-1) = 6.31 and r(2) = -16.88
Step-by-step explanation:
* Lets read the problem and solve it
- Evaluate means find the value, so evaluate r(x) means find the value
of it at the given values of x
∵ r(x) = -0.21x³ + x² - 8.1x - 3
∵ x = -1 and x = 2
- Then find r(-1) by substitute x by -1 and find r(2) by substitute x by 2
# At x = -1
∴ r(-1) = -0.21(-1)³ + (-1)² - 8.1(-1) - 3
∴ r(-1) = -0.21(-1) + (1) - 8.1(-1) - 3
∴ r(-1) = 0.21 + 1 + 8.1 - 3
∴ r(-1) = 6.31
# At x = 2
∴ r(2) = -0.21(2)³ + (2)² - 8.1(2) - 3
∴ r(2) = -0.21(8) + (4) - 8.1(2) - 3
∴ r(2) = -1.68 + 4 - 16.2 - 3
∴ r(2) = -16.88
* r(-1) = 6.31 and r(2) = -16.88