Answer:
[tex]25\leq 27[/tex]
Explanation:
1. Starting inequality:
[tex]-125\geq -135[/tex]
2. Divide both sides by [tex]-5[/tex]
3. Rule
When you divide an inequality by a negative number, the inequality symbol has to be changed:
> changes to << changes to >≤ changes to ≥≥ changes to ≤4. Solution
Thus, when dividing by -5 change the inequality symbol ≤ to ≤
[tex]\dfrac{-125}{-5}\leq \dfrac{-135}{-5}\\\\\\25\leq 27[/tex]
Which number is smaller in between -1 and -0,25
Answer:
-1 is the smallest according to this question
pls help on number 11 i will mark brainliest easy math
Answer:
quadrilateral; irregular
Step-by-step explanation:
Line l and line k are perpendicular. Line l has a slope of 3. Line k contains the points (5, 8) and (2,
y). What is the value of y?
Answer:
y = 9
Step-by-step explanation:
Calculate the slope m of line k using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 8) and (x₂, y₂ ) = (2, y)
m = [tex]\frac{y-8}{2-5}[/tex] = [tex]\frac{y-8}{-3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]
The slope of line l is m = 3, thus slope of line k is
m = - [tex]\frac{1}{3}[/tex]
Equating the 2 slopes for line k
[tex]\frac{y-8}{-3}[/tex] = - [tex]\frac{1}{3}[/tex] ( multiply both sides by - 3 )
y - 8 = 1 ( add 8 to both sides )
y = 9
To find the value of y, we can use the fact that the slopes of Perpendicular lines are negative reciprocals of each other. Using the given information and equations, we can solve for y.
To determine the value of y, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Since line l has a slope of 3, the slope of line k would be -1/3. We can use the slope-intercept form, y = mx + b, to find the equation of line k.
Substituting the coordinates (5, 8) and the slope -1/3 into the equation, we can solve for y.
Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point (2, y). We can rearrange this equation to get y = mx + b form, substitute the values, and solve for y to find the value of y.
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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
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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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.
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
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
Simplify this expression
a) 2a + 5a
Answer:
7a
Step-by-step explanation:
twice the difference of a number and 2 is at most -27
When we say "a is at most b" we mean that "a is less than or equal to b" or "a is not greater than b". So let's solve this problem as follows:
Step 1. Twice the difference of a number and 2
Let's call that unknown number as n. Then, twice the difference of a number and 2 is:
[tex]2(n-2)[/tex]
Step 2. Twice the difference of a number and 2 is at most -27
[tex]2(n-2)\leq -27[/tex]
_________________________________________
So the mathematical form of the statement twice the difference of a number and 2 is at most -27 is:
[tex]\boxed{2(n-2)\leq -27}[/tex]
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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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
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
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.
Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2?
Answer:
A (0,3)
Step-by-step explanation:
The given trapezoid has vertices:
(0,6), (7,12), (7,9) and (0,12).
We want to choose from the given options, a point that is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2.
Note that the mapping for such a dilation is:
[tex](x,y)\to( \frac{1}{2} x, \frac{1}{2} y)[/tex]
This implies that:
[tex](0,6)\to(0,3)[/tex]
[tex](7,12)\to(3.5,6)[/tex]
[tex](7,9)\to(3.5,4.5)[/tex]
[tex](0,12)\to(0,6)[/tex]
Therefore correct choice is (0,3)
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:
Please help
5 points up for grabs
Answer:
490
Step-by-step explanation:
oh lord here we go again
get the area of all signs again
5 x 5 = 25
theres 2 of those squares so make that 50
8 x 5 = 40
theres 4 of those sides so 40 x 4 = 160
10 x 10 = 100
theres two of those so its 200
2 x 10 = 20
4 of these so 80
add all the final ones
50 + 160 + 200 + 80 = 490
Kayla has 8 red tennis balls 6 green tennis balls and five blue tennis balls can kala write a multiplication equation to find out how many tennis balls has she has it in all
Answer:
Equation for total number of balls = 8x+6x+5x =19x where x represent a single tennis ball.
Step-by-step explanation:
Given that Kayla has;
8 red tennis balls
6 green tennis balls
5 blue tennis balls
Let;
red tennis ball be r
green tennis balls be g
blue tennis balls be b
The total number of tennis balls is 8+5+6=19 balls
Multiplication is a repeated form of addition where ;
5*5*5 = 3*5= 5+5+5= 15
In this case, r+g+b=19 but r ,g and b are not repeated thus applying multiplication equation will not give the sum of the balls
However if you let a single ball to be represented by x then a single ball x will be multiplied by the number of balls in that category to get the total number of balls per color
For red balls= 8x
For green balls=6x
For blue balls=5x.
Total number of balls = 8x+6x+5x =19x where x represent a single tennis ball.
To find the total number of tennis balls Kayla has, she needs to add the number of each color of balls together, not multiply. When she adds 8 red, 6 green, and 5 blue balls, she gets 19 tennis balls in total.
Explanation:In this case, Kayla doesn't need to use a multiplication equation to find out the total number of tennis balls she has. Rather, she just needs to add the numbers together. Kayla has 8 red tennis balls, 6 green tennis balls, and 5 blue tennis balls. So, to figure out how many tennis balls she has in total, she simply adds these numbers together: 8 + 6 + 5 = 19 tennis balls in total.
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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.
URGENT!!!
The tallest building in Africa is the Carlton Centre in Johannesburg, South Africa. What is the distance from the top of this 738 ft building to the horizon to the nearest mile?
(Hint: 5,280 ft = 1 mi; radius of Earth = 4,000 mi)
Answer:
its near 1 mile or half a mile
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.
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
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
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 )
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.
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]
Tegan bought 1 1/6 metres of ribbon. She needs 2/5 metres to wrap her brothers present and 3/4 metres to wrap her sisters present. Did she buy enough ribbon?
Answer:
Yes
Step-by-step explanation:
2/5 + 3/4 = [2(4) + 3(5)]/20
= 23/20 = 1 3/20
1 3/20 = 1 9/60
1 1/6 = 1 10/60
1 1/6 > 1 3/20
Find the volume of the cone to the nearest whole number. Radius is 2 and height is 4
Volume of the cone is 17 cm³
Step-by-step explanation:
Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 2 inches and h = 4 cm.Volume = 1/3 × 3.14 × 2² × 4
= 16.75 cm³ ≈ 17 cm³ (rounding off to nearest whole number)
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!