Answer:
[tex]5 {y}^{2} - 80[/tex]
Step-by-step explanation:
The given polynomials are:
[tex]5 {y}^{2} - 80[/tex]
and
[tex]y + 4[/tex]
Let us factor the first polynomial to get:
[tex]5 {y}^{2} - 80 = 5( {y}^{2} - 16)[/tex]
We need to rewrite as difference of two squares:
[tex]5 {y}^{2} - 80 = 5( {y}^{2} - {4}^{2} )[/tex]
We can now factor to get:
[tex]5 {y}^{2} - 80 = 5( {y} - 4)(y + 4)[/tex]
So the least common multiple of
[tex]5( {y} + 4)(y - 4) \: and \: (y + 4) \: is \: 5( {y} + 4)(y - 4) = 5 {y}^{2} - 16[/tex]
l
Simplify this expression
a) 2a + 5a
Answer:
7a
Step-by-step explanation:
Given the equations ‘2x+ 4/3y=1’ and ‘y-9/13x=9’, by what factor would you multiply the first equation so that combining the two equations would eliminate x?
A- ‘-9/26’
B- ‘9/26’
C- ‘1/2’
D- ‘-9/13’
The right answer is Option B: 9/26
Step-by-step explanation:
Given equations are;
[tex]2x+\frac{4}{3}y=1[/tex] Eqn 1
[tex]y-\frac{9}{13}x=9[/tex] Eqn 2
For eliminating x, we will make the variables equal with opposite signs.
In Eqn 1;
We will multiply Eqn 1 by 9/26 to get +9/13x.
[tex]\frac{9}{26}(2x+\frac{4}{3}y=1)\\\\\frac{9}{13}x+\frac{6}{13}y=\frac{9}{26}[/tex]
Therefore;
We will multiply Eqn 1 by 9/26.
The right answer is Option B: 9/26
What is the length of line segment QP? Round to the
nearest unit.
O
O
O
o
13 units
17 units
18 units
20 units
Answer:
[tex]QP=20\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
Let
O ---> the center of the circle
we have that
Line segment QP is tangent to the circle
That means
OQ (radius) is perpendicular to segment QP
OQP is a right triangle
Applying Pythagorean Theorem
[tex]OP^2=OQ^2+QP^2[/tex]
we have
The radius is equal to
[tex]r=24/2=12\ units[/tex] ----> the radius is half the diameter
[tex]OP=r+NP=12+11.5=23.5\ units[/tex]
[tex]OQ=r=12\ units[/tex]
substitute
[tex]23.5^2=12^2+QP^2[/tex]
[tex]QP^2=23.5^2-12^2[/tex]
[tex]QP^2=408.25[/tex]
[tex]QP=20\ units[/tex]
Answer:20 units
Step-by-step explanation:
Help please !!!!!!!!!!!!!!!!!!!!!
Answer:
The last one
Step-by-step explanation:
volume is v= [tex]\pi r^{2} h[/tex] . this means volume is mathematical number pi, times the (radius squared), times the height. the radius is marked at the yellow line, and the height on the side. this means you would have v = [tex]\pi[/tex][tex](x+2)^{2}[/tex][tex](3x+8)[/tex]
first, lets work out [tex](x+2)^{2}[/tex]. we can rewrite this as (x+2)(x+2). we are going to use a system called FOIL. this stands for First Outside Inside Last. This means we are going to take the first number from both and multiply them together, then the outside, inside, and last. so, for first, we will multiply x and x and then we have [tex]x^{2}[/tex], for outside we multiply x and 2 and we get [tex]2x[/tex], for inside we multiply 2 and x and we get [tex]2x[/tex], and for last we multiply 2 and 2 and we get [tex]4[/tex]. then we add all these together. [tex]x^{2} + 2x + 2x + 4[/tex]. then simplify like terms to get
[tex]x^{2} + 4x + 4[/tex]. now, we can't forget about our times [tex]\pi[/tex] and (3x+8)
this means we have to multiply [tex]x^{2} + 4x + 4[/tex] by those two.
it would look like this: ([tex]x^{2} + 4x + 4[/tex])(3x+8)[tex]\pi[/tex]
so now we are going to multiply the other two sets of parentheses
we multiply each number from the first set to each number in the second set.
A successful author invests some of his earnings in two accounts for 1 year. the function f(x)=.05 models the interest he earns on x dollars invested in the first account. the function g(x)=.075(x+2500) models the interest he earns from the second account, in which he invests $2500 more than in the first account.
Evaluate (f+g)(18,500) and interpret what it means in this situation
The value of [tex](f+g)(18500)[/tex] is [tex]\Dollar 16675[/tex] dollars.
Interest earning :The interest he earns on x dollars invested in the first account is given by,
[tex]f(x)=0.05x[/tex]
The interest he earns from the second account,
[tex]g(x)=0.075(x+2500)[/tex]
[tex]f(x)+g(x)=0.05x+0.75(x+2500)\\\\f(x)+g(x)=0.05x+0.75x+1875\\\\f(x)+g(x)==0.8x+1875\\\\(f+g)(18500)=(0.8*18500)+1875\\\\f(x)+g(x)=14800+1875\\\\f(x)+g(x)=16675[/tex]
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Liam's last grocery bill was $105. This week, his bill was $85. Calculate the percent change. Round to the nearest hundredth.
Answer:
.199 or 20% (.20)
Step-by-step explanation:
Percentage change:
p=(85-105)/105=-20/105=-19.047%
Rounded value: -19.05%
The minus sign indicates a decrease in amount spent.
9. D is 20 + h
But help :)
Answer:
8. D 269.6
9. A 20 +10h
Step-by-step explanation:
8. The large rectangle is 4+6.4+4+6.4 = 20.8 width and 10.5 length. The area is
A = l*w = 20.8* 10.5 =218.4
The top rectangle is 6.4 width and length is 4
A = l*w =6.4*4 =25.6
The same is true for the rectangle on the bottom.
Add the three rectangles together to get the total surface area
218.4+25.6+25.6 =269.6
9. The plant is 20 inches tall
It grows 2h inches a week for 4 weeks
20 +2h*4
20 +8h
It grows h inches a week after 4 weeks
At 6 weeks, that is 2 weeks of growth
The growth is h *2
Add that to the previous total
20 +8h +2h
20 +10h
Divide 68p in the ratio 1 : 2 : 1
Answer:
17p:34p:17p
Step-by-step explanation:
68p/(1+2+1)=
17p(1):17p(2):17p(1)=
17p:34p:17p
Find the area of the following geometric figure
area of a triangle with
ase of 15 m and altitude of 12 m.
The area of the triangle is 90 m²
Explanation:
Given that the base of the triangle is 15 m
The altitude of the triangle is 12 m
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]Area=\frac{1}{2}bh[/tex]
where b is the base and h is the altitude
Thus, we have,
[tex]b=15[/tex] and [tex]h=12[/tex]
Substituting the values in the above formula, we get,
[tex]Area=\frac{1}{2}(15)(12)[/tex]
Multiplying the terms, we get,
[tex]Area=\frac{180}{2}[/tex]
Dividing, we get,
[tex]Area=90 \ m^2[/tex]
Therefore, the area of the triangle is 90 m²
I'LL GIVE YOU BRAINLIEST!!
Which scatterplot suggests no relationship between x and y?
A) II only
Eliminate
B) III only
C) I and III only
D) II and III only
Answer:
B) III only, it doesn't suggests relationship between x and y.
An electrician cut 36 feet of wire into sections that were each 8 1/2 feet long. After cutting, how many pieces of wire did the contractor have?
pls help on number 11 i will mark brainliest easy math
Answer:
quadrilateral; irregular
Step-by-step explanation:
ted, sam, and jack can do a piece of work in 15, 12 and 20 days respectively. they started the work together, but jack left after 2 days. in how many days will the remaining work be completed by ted and sam?
Answer:
the answer was 24
Step-by-step explanation:
What value does the 3 represent in the number 16.344?
Answer:
00.300
Step-by-step explanation:
What value does the 3 represent in the number 16.344
The 3 in the number 16.344 represents 0.003, since it's located on the third decimal place. It contributes three-thousandths to the total value. The position of the number changes the value it represents.
Explanation:The value of 3 in the number 16.344 is represented as 0.003 in decimal place value. This is because it is situated in the third digit after the decimal point, signifying that it contributes the amount equal to three thousandths (0.003) to the total value of the number. For example, in using the concept of Six significant figures, we can say the number 16.344 has five significant figures, that is, the digits that give us precise information about the magnitude of the number - these digits being 1, 6, 3, 4 and 4.
It's also worthwhile to note that the placement of the digit 3 in the number 16.344 is different from a 3 that is located at other decimal places. For instance, if we look at the number 16.3443, the second 3 after the decimal point represents three ten-thousandths (0.0003) contribution to the total value of the number.
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Does 9,12,15 form a right triangle
Answer:
Yes.
Step-by-step explanation:
Note that 15^2 = 122^ + 9^2 ( 225 = 144 + 81 = 225).
So by the Inverse of Pythagoras Theorem it is a right triangle.
The given values of side makes a proper right angle triangle.
To determine if the three given side lengths, 9, 12, and 15, form a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's check if this holds true for the given side lengths:
[tex]9^2 + 12^2 = 81 + 144 = 225\\\\15^2 = 225[/tex]
The sum of the squares of the two shorter sides, 9 and 12, is equal to the square of the longest side, 15. This satisfies the Pythagorean theorem.
Therefore, the side lengths 9, 12, and 15 do form a right triangle.
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Larry had $480 he used to thirds of it to buy an electric band he also bought tea set for 60 how much money did he have left
Answer:
Here's our equation:
480 * 1/3 - 60 = []
The 1/3 comes from 1 - 2/3 = 1/3 for note, as that's how much of her money is left after the fan's purchased. (if you're unsure, you can multiply 480 and 2/3 together, and then subtract that amount from 480, and you'll see you end up with the same answer as below)
The order of operations means we deal with the 480 * 1/3 first.
480 * 1/3 → 480/3 = 160
Next is subtraction:
160 - 60 = 100
So Mrs. Ricci has $100 left.
Step-by-step explanation:
Rotate (-4,8) 90cc. What is the new order pair?
Answer:
(- 8, - 4 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), thus
(- 4, 8 ) → (- 8, - 4 )
Which number is smaller in between -1 and -0,25
Answer:
-1 is the smallest according to this question
b2+16b+64
-3k3+15k2-6k
Answer:
1. [tex](b+8)^{2}[/tex]
2. [tex]-3k(k^{2} -5k+2)[/tex]
3. [tex](3x-1)(x-5)[/tex]
Step-by-step explanation:
1. Both [tex]x^{2}[/tex] and 64 are perfect squares, meaning [tex]16b[/tex] is twice the product of x and 8. Since all signs are positive, the equation would be: [tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]. Let [tex]a=x[/tex] and [tex]b=8[/tex]. Answer: [tex](b+8)^{2}[/tex] or [tex](b+8)(b+8)[/tex].
2. Since -3 is a factor of all 3 terms, factor out the -3 which makes, [tex]-3(k^{2} +5k^{2} -2k)[/tex] . K is also a common factor, so you would factor that out too, [tex]-3k(k^{2} -5k-2)[/tex]. Then simply, find the two factors whose product is -2 and whose sum is -5. Answer: [tex]-3k(k^{2} -5k+2)[/tex].
3. By factoring [tex]3x^{2} -16x+5[/tex], you would break the expressions in the group=[tex](3x^{2} -x)+(-15x+5)[/tex]. Then, factor out "x" from [tex]3x^{2} -x: x(3x-1)[/tex]. Factor out "5" from [tex]-15x+5:-5(3x-1)[/tex] = [tex]x(3x-1)-5(3x-1)[/tex]. Finally, factor out the common term "3x-1" = [tex](3x-1)(x-5)[/tex]
Explain how the product 1\2 ×1\3 relates to the model
Final answer:
The product 1/2 x 1/3 equals 1/6, which can be visualized using a two-dimensional model where a rectangle is divided into halves and then thirds, resulting in 1/6 of the total area.
Explanation:
The product 1/2 times 1/3 can be understood through a two-dimensional model. If you take a rectangle and divide it into 2 equal parts, taking 1/2 of the whole, and then divide one of those halves into 3 equal parts, taking 1/3 of that half, you will have 1 out of the 6 equal parts of the original rectangle, which is 1/6, the product of 1/2 and 1/3.
To visualize this process, imagine a bar or a piece of chocolate that is first divided down the middle, and then one of those halves is divided into 3 equal pieces.
Taking one of these smaller pieces represents 1/6 of the original chocolate bar. In mathematical terms, when we multiply fractions, we multiply the numerators ( 1 times 1) to get the numerator of the product, and the denominators (2 times 3) to get the denominator of the product, yielding 1/6 as the answer. This demonstrates the first partial product principle, where in this case the third vector (1/3) is multiplied by the scalar product of 1/2.
A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.
Answer:
They paid $4.00 per ticket
Step-by-step explanation:
Step 1: Convert words into an inequality
A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.
6t + 3 = 27
Step 2: Solve for t/tickets
6t + 3 = 27
6t + 3 - 3 = 27 - 3
6t / 6 = 24 / 6
t = 4
Answer: They paid $4.00 per ticket
Answer:
4
Step-by-step explanation:
3 - 27 = 24
24 ÷ 6 = 4
4 · 6 = 24
3 + 24 = 27
A = $27
what fraction is equivalent to 3/4
Answer:
6/8
Step-by-step explanation:
3/4 = 6/8 = 9/12 and so on
Answer:
9/12
Step-by-step e
A triangular prism has a volume of 350 cubic meters. If the dimensions are tripled what is the volume of the new
prism?
Answer:
9450 m³
Step-by-step explanation:
(S1/S2)³ = V1/V2
3³ = V1/350
New Volume = 27 × 350
= 9450 m³
What is the measurement of the unknown fourth interior angle of this quadrilateral? A) 80° B) 95° C) 100° D) 115°
Answer: The Answer is 100, sorry that you got it so late.
Step-by-step explanation:
What I did
1. Find the difference between the numbers
2. Look through answer choices
3. Because the difference of 80 and 75 was 5, 105 would be 100.
Sorry if this doesn't make sense.
List all the multiples of 8 that are less than or equal to 100. List all the multiples of 12 that are less than or equal to 100. What are the common multiples of 8 and 12 from the two lists?
Answer:
24,48,72,96
Step-by-step explanation:
Multiples of 8
8, 16,24,32,40,48,56,64,72,80,88,96
Multiples of 12
12,24,36,48,60,72,84,96
Common multiples
24,48,72,96
Answer:
See below.
Step-by-step explanation:
"List all the multiples of 8 that are less than or equal to 100."
0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
"List all the multiples of 12 that are less than or equal to 100."
0, 12, 24, 36, 48, 60, 72, 84, 96
Common multiples: 0, 24, 48, 72, 96
If ABCD is a parallelogram,which statement would prove that ABCD is a rhombus?
(Picture is the choices to the question)
To prove ABCD is a rhombus, showing that all sides of parallelogram ABCD are equal in length would suffice.
Explanation:If ABCD is a parallelogram, to prove that it is a rhombus, a statement that would suffice is that all four sides of the parallelogram are of equal length.
This is because a rhombus is defined as a parallelogram with four congruent sides. If any one of its diagonals bisects an angle of the parallelogram, or its diagonals are perpendicular, or its diagonals are of the same length, these conditions would not exclusively prove it to be a rhombus, although they are properties of a rhombus. However, the definition of a rhombus centers on the equality of all sides.
Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.
The correct option is (B).
To prove that a parallelogram is a rhombus, you need to show that all four sides are of equal length. A parallelogram has opposite sides that are equal and parallel, but for it to be a rhombus, every side must be equal in length to every other side.
The statement options you might have in your image could be something like:
a. Diagonals are perpendicular (AC ⊥ BD)
b. Adjacent angles are equal (∠ABC ≅ ∠CDA)
c. One pair of opposite sides are equal (AB ≅ CD)
d. Diagonals are equal (AC ≅ BD)
From these options:
- Option a: If the diagonals are perpendicular, it's an indication that the parallelogram could be a rhombus, but it's not conclusive proof because a rectangle also has perpendicular diagonals.
- Option b: Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.
- Option c: Having one pair of opposite sides that are equal is already a property of a parallelogram and does not prove it's a rhombus.
- Option d: Equal diagonals would be a property of a rectangle, not necessarily a rhombus.
The conclusive proof that a parallelogram is a rhombus would be if you can show that all sides are of equal length (not provided in the typical options above), or if the diagonals are perpendicular and bisect each other into equal segments. This latter property is unique to a rhombus among parallelograms. If this were one of the choices, it would be the correct answer.
Since I can't see the options, please review them and look for the one that indicates all four sides are of equal length or that the diagonals bisect each other into equal segments and are perpendicular. That would be the correct choice to prove the parallelogram is a rhombus.
What is the mixed number as a fraction of 5 3/4
Answer:
23/4
Step-by-step explanation:
multiply the whole number (5) by the denominator (4) and add your numerator (3), which for you is 23, then put that over your denominator (4). so it would be 23/4 :)
Well I'm a bit confused since 5 3/4 is a mixed number. Please elaborate!
What is the surface area of this triangular prism rounded to the nearest tenth? A) 48.6km2 B) 63.4 km2 C) 72.6 km2 D) 84.4 km2
Correct option B)[tex]63.4km^2[/tex] .
Step-by-step explanation:
We have the following figure attached as shown below.
Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:
2 similar right angled surfaces
We know that area of triangle = [tex]\frac{1}{2} b(h)[/tex]
⇒ [tex]area = \frac{1}{2} b(h)[/tex]
⇒ [tex]area = \frac{1}{2} (3.6)(7.7)[/tex]
⇒ [tex]area = 13.86km^{2}[/tex]
But there 2 such surfaces so , [tex]area = 2(13.86) = 27.72km^2[/tex]
3 rectangular surfaces
Area of rectangle = [tex]length(breadth)[/tex]
⇒ [tex]area_1 = 3.6(1.8)[/tex]
⇒ [tex]area_1 = 6.48km^2[/tex]
⇒ [tex]area_2= 7.7(1.8)[/tex]
⇒ [tex]area_2 = 13.86km^2[/tex]
⇒ [tex]area_3 = 8.5(1.8)[/tex]
⇒ [tex]area_2 = 15.3km^2[/tex]
Total area =[tex]6.48 + 13.86 + 15.3 = 35.64km^2[/tex]
Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:
[tex]Area = 27.72+35.64 = 63.36km^2[/tex] = [tex]63.4km^2[/tex]
Correct option B)[tex]63.4km^2[/tex] .
Answer:
It is B.
Step-by-step explanation:
Trust me it's B
How to solve 16 * 12.5
Answer: 200
Step-by-step explanation:
First I would do it like this.
12.5
X. 16
—————-
6 times 5 is 0, carry the 3, 6 times 2 is 12 and add 3 from the other which is 15, put the 1 from the 15 to the one next to the 12. 6 times 1 is 6 plus 1 is 7 which now you have 750. 5 times 1 is 5, 2 times 1 is 2, 1 times 1 is 1. It should look like this now.
12.5
X 16
—————
750
+ 1250
——————-
Which is 8750 but wait. Where is the decimal? Well, there is only one number behind the decimal so it is 875.0 or 875.
can someone please help me with this question What is the minimum value of the quadratic function f(x) = x² - 2x + 7
minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).
Step-by-step explanation:
Here we have , f(x) = x² - 2x + 7 or [tex]f(x) = x^2 - 2x + 7[/tex] . We need to find the minimum value of f(x) for which we need to differentiate it one time and equate it to zero . Value of x at which first differentiation of f(x) is zero will be the minimum value of function . Let's solve this:
[tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2 - 2x + 7)}{dx}[/tex]
⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2)}{dx} - \frac{d(2x)}{dx} + \frac{d(7)}{dx}[/tex]
⇒ [tex]\frac{df(x)}{dx} = 2x-2 = 0[/tex]
⇒ [tex]2x-2 = 0[/tex]
⇒ [tex]x =1[/tex]
Now, value of function at x=1 is :
[tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]f(1) = 1^2 - 2(1) + 7[/tex]
⇒ [tex]f(1) = 8- 2[/tex]
⇒ [tex]f(1) = 6[/tex]
Therefore, minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).
The minimum value of the quadratic function f(x) = x² - 2x + 7 is 6, which occurs at x = 1, as determined by finding the vertex of the parabola.
Explanation:The minimum value of the quadratic function f(x) = x² - 2x + 7 can be determined by finding the vertex of the parabola represented by the function. This is because the graph of a quadratic function is a parabola, and if the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents the minimum point.
To find the vertex, use the formula -b/2a to determine the x-coordinate of the vertex. For the function f(x), the value of 'a' is 1 and 'b' is -2. Substituting these values gives us the x-coordinate of the vertex as x = -(-2)/(2*1) = 1. Substituting x = 1 back into the function f(x), we get the y-coordinate of the vertex, which is the minimum value of the function: f(1) = (1)² - 2*(1) + 7 = 6.
Therefore, the minimum value of the quadratic function f(x) is 6, occurring at x = 1.