Answer:
2(4ax+2bx+2a+5b)
Step-by-step explanation:
Which value of m will create a system of parallel lines with no solution?
y=mx-6
8x-4y=12
Answer: y = 2x - 6
Step-by-step explanation:
Let us turn the second given equation into slope-intercept form to match the first equation.
8x - 4y = 12
8x - 12 = 4y
4y = 8x - 12
y = 2x - 3
Now, parallel lines have the same slope. This is the m value.
y = 2x - 3
\/
y = mx - 6
y = 2x - 6
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In the diagram shown, the area of the triangle is 44.3m². If b = 14.1m and the angle at C = 48°, work out x. Round to 1 DP. X C b
If the height of the triangle will be 6.28 meters. Then the value of x will be 8.46 meters.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In the diagram shown, the area of the triangle is 44.3 m².
If b = 14.1 m and the angle at C = 48°.
Then the value of x will be
The height of the triangle will be
A = 1/2 × B × H
44.3 = 1/2 × 14.1 × h
h = 6.28 m
Then the value of x will be
sin 48° = 6.28 / x
x = 8.455 ≈ 8.46 m
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The number of boys who signed up to play winter basketball is 175 percent of what it was last year. if 320 boys played winter basketball last year, how many signed up to play this year?
The number of boys signed up to play basketball this year is 560.
Given that, the number of boys who played basketball last year = 320.
We need to find the number of boys signed up to play basketball this year.
What is a percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Now, the number of boys signed up to play basketball this year = 175 per cent of what it was last year.
So, the number of boys signed up to play basketball this year = 175% of 320
[tex]=\frac{175}{10} \times 320=1.75 \times 320=560[/tex]
Therefore, the number of boys signed up to play basketball this year is 560.
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please narrate every step you make and make a 2 column proof!
thank you!!
Hang on ,it is already proven through given .
So The proof is of one line only
ray FEH bisects <DFG (Given)Hence proved .
The pie chart below shows how the annual budget for a certain companies divided by department is a total budget is 15,000,000 what amount is budgeted for sales research and engineering combined
If the amount of budget for media and sales combined is $25,000,000. Then the total annual budget will be $125,000,000.
The complete question is attached below.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
The pie chart below shows how the annual budget for a certain company divided by department.
If the amount of budget for media and sales combined is $25,000,000.
Then the total annual budget will be
Let x be the total annual budget.
17% + 3% = 25,000,000 / x
20% = 25000000 / x
0.20 = 25000000 / x
x = $125,000,000
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What is the quadratic equation for 0=-2x+3x^2
x = 2/3 , 0 .
Question :
[tex] {3x}^{2} - 2x = 0[/tex]
use quadratic formula :
[tex]x = \frac{( - b)± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Solution :
[tex]a {x}^{2} + bx + c = 0 \\ a = 3 \\ b = - 2 \\ c = 0[/tex]
[tex]x = \frac{ - ( - 2)± \sqrt{ { (- 2)}^{2} - 4 \times 3 \times 0} }{2 \times 3} \\ \\ x = \frac{2± \sqrt{4 - 0} }{6} \\ \\ x = \frac{2± \sqrt{4} }{6} \\ \\ x = \frac{2± 2}{6} [/tex]
separate into two equations :
[tex]x = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} .[/tex]
[tex]x = \frac{2 - 2}{6} = \frac{0}{6} = 0.[/tex]
the values of x are 2/3 and 0 .
10) Find the perimeter of the shape below, which has been formed from two quarter circles, [1]
rounding your answer to 3 significant figures
P
8.7 cm
What is the solution for x in the equation?
5
3x + 4 =
2
OA. * = -4
OB. * = 4
12
O C.
OD.
X
x =
-1/7/20
Equations are separated by an equal sign. The value of x is given as -6/5
Equations and valuesGiven the equations below;
5(3x + 4) = 2
Expand
5(3x) + 5(4) = 2
15x +20 = 2
Subtract 2 from both sides
15x = 2 - 20
15x = -18
x = -18/15
x = -6/5
Hence the value of x is given as -6/5
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2. If D is the midpoint of segment AB, explain using transformations why AC = BC. Use complete sentences. (10 points)
AC is equal to BC by the corresponding side of a congruent triangle.
What is a line segment?
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
The midpoint of a line segment means a point that lies in the mid of the given line segment.
If D is the midpoint of segment AB, then AD = BD.
So in a triangle ACD and BCD
AD = BD (by midpoint D)
angle ADC = angle BDC = 90
CD = CD (common)
Therefore, triangle ACD and BCD are congruent.
Hence, AC = BC by the corresponding side of a congruent triangle.
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a sunflower has increased in height from 72.4cm to 86.2 cm. what is the percentage increase?
Answer:
initial hieght = 72.4 cm
final hieght = 86.2 cm
change in hieght = 9.8 cm
percentage increase = (9.8 ÷ 72.4 ) * 100 = 13.59 %
The expression 2 (a + b) = -8.1 for certain values of a and b. Find the value of the following expressions for the same values of a and b: 4a+4b
If we put a=0 and b=-4.05 then the expression 4a+4b becomes -16.2 and when we put a=-4.05 and b=0 then the expression becomes -16.2.
Given 2 (a + b) = -8.1
Because no relationship between a and b is given so we can put any value of one variable to determine the value of another variable.
If we put a=0 in 2(a+b) =-8.1 then b=-4.05
If we put b=0 then a =-4.05.
We need to put these values in 4a+4b
when a=0 b=-4.05
4a+4b=4*0+4*-4.5
=-16.2
when b=0 and a=-4.05
4a+4b=4*-4.05+4*0
=-16.2
Hence for a=0,b=-4.5 the value of 4a+4b equals -16.2 and for a=-4.05 and b=0 the function equals -16.2.
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Someone help me with 4 pleaseeeeee
Answer:
C
Step-by-step explanation:
Use the equation [tex]a^2 + b^2 = c^2[/tex]
Input the numbers----> [tex](2865)^2 +(4550)^2=c^2[/tex]
Simplify ----> [tex]28910725=c^2[/tex]
Find the square root------->[tex]5376.9=c[/tex]
What's the length of an arc with a central angle of 120and a radius of 5 inches?
Answer:
(10/3)π units
Step-by-step explanation:Mark if it is correct
Answer:
[tex]\frac{10\pi }{3}[/tex] inches
≈ 10.5 inches
Step-by-step explanation:
The formula for arc length is as follows:
Arc length = [tex]\frac{\theta}{360} * 2\pi[/tex]
[tex]\frac{120}{360} * 10\pi \\= \frac{1}{3} * 10\pi \\= \frac{10\pi}{3}[/tex]
Hope this helps and feel free to mark this as brainliest!
Answer: 5 x 4/7
Full explanation.
Answer:
20/7
Step-by-step explanation:
5×4/7
numerator5×numerator4=20
denominator 7×denominator1=hence,answer is
20/7
Solve for x
((x + 3)/4) + (((2x - 12) - 1)/3) = 1
Answer:
x=5
Step-by-step explanation:
[tex]((x+3)/4)+(((2x-12)-1)/3)=1\\\frac{x+3}{4} +\frac{2x-12-1}{3} =1\\\frac{x+3}{4} +\frac{2x-13}{3} =1\\[/tex]
Now we have to cross multiply the denominator to progress further.
[tex]\frac{3(x+3)}{4*3} +\frac{4(2x-13)}{3*4} =1\\\frac{3x+9}{12} +\frac{8x-52}{12} =1\\\frac{3x+9+(8x-52)}{12} =1\\\frac{3x+9+8x-52}{12} =1\\\frac{11x-43}{12} =1\\11x-43=12\\11x=43+12\\11x=55\\x=\frac{55}{11} \\=5[/tex]
one angle of a triangle measures 80° more than the smallest, while a third angle is twice the smallest. whats the measure of each angle?
Answer: The measure of each angle is 105°, 50°, and 25°.
Step-by-step explanation: The first step in solving this is writing down what you know.
In the phrase it tells you that "one angle of a triangle measures 80 more than the smallest", so we can say that one angle = 80 + smallest angle.
This can be simplified more to x = 80 + y
x = One Angle
y = Smallest Angle
Then if we continue with the phrase it says "a third angle is twice the smallest", so we can say that a third angle = 2(Smallest Angle).
This can be simplified more to z = 2(y)
z = Third Angle
We also know that a triangles angles add up to 180°, so we know x + y + z = 180.
So, with these equations we can now solve for x, y, and z.
The easiest way would be to simply just plug in x and z straight into the 180 equation as follows.
x = 80 + y
z = 2(y)
180 = x + y + z
180 = (80 + y) + y + (2y)
180 = 80 + 4y
100 = 4y
y = 25
Then we can use y to solve for the other two equations.
z = 2(25) x = 80 + 25
z = 50 x = 105
After completing that you are left with the three angles of the triangle, 25, 50, and 105.
2x+y=8
y+3z=5
z+2w=1
5w+3x=9
what is x,y,z,w
Answer:
Systems of equations:
x=3
y=2
z=1
w=0
Look at the diagram. Which of the following is another name ∠2?
∠CDB
∠BCD
∠DCB
∠DBC
The other name for angle 2 is ∠DBC
The correct option is (D)
What is Angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
We know that while naming the angle we have to consider the point where the angle is made should be at center.
Hence, the angle 2 can also be written as ∠DCB.
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These points are linear.
Find the slope.
x
012345
y 3 6 9 12 15 18
slope = [?]
Answer:
Step-by-step explanation:
Which of the following describes point D?
O (-4,0)
O (4,0)
O (0,4)
O (0,-4)
Answer:
The answer is C (0,4)
Step-by-step explanation:
Looking at the graph we have to find a point (x,y) of D.
Find point D. It is on the y-axis, but which one? Positive/Negative y-axis.
It appears to be on the positive y-axis.
Now we have to choose either option C or D.
Option C seems like the best choice since the point is (x,y) is (0,4) on the positive y-axis.
Option D is quite the opposite of point D since the point (0, -4) is on the negative y-axis.
The answer is C. (0,4)
Calculate the sum of each expression. Arrange the expressions in the order of their value from largest to smallest.
92 + ( -5 )
2+2
Answer:
6
Step-by-step explanation:
Answer:
92 + ( -5 ) , 2+2
Step-by-step explanation:
1) 92 + ( -5 )
= 92 - 5
= 87
2) 2 + 2 = 4
What are the zeros of the function f(x) = x4 − x2 − 2?
±3, ±i
±2, ±i
positive or negative square root of 2 comma ±i
positive or negative square root 3, ±i
Answer:
x = ± [tex]\sqrt{2}[/tex] , x = ± i
Step-by-step explanation:
f(x) = [tex]x^{4}[/tex] - x² - 2
to find the zeros , equate f(x) to zero , that is
[tex]x^{4}[/tex] - x² - 2 = 0
using the substitution u = x² , then
u² - u - 2 = 0 ← in standard form
(u - 2)(u + 1) = 0 ← in factored form
equate each factor to zero and solve for u
u - 2 = 0 ⇒ u = 2
u + 1 = 0 ⇒ u = - 1
convert u back into terms of x
x² = 2 ( take square root of both sides )
x = ± [tex]\sqrt{2}[/tex]
x² = - 1 ( take square root of both sides )
x = ± [tex]\sqrt{-1}[/tex] = ± i
Answer: Positive or negative square root of 2, ±i
Proof o fvalidity is shown below.
Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question.
Which cylinder pressure will Jillian need if she plans to fill 90 balloons?
According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons. Option D is correct.
What is pressure?The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure. The force involved vertically to the surface of an object per unit area is pressure.
It is denoted by P. The pressure relative to the ambient pressure is known as the gauge pressure.
The complete question is:
Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question. Which cylinder pressure will Jillian need if she plans to fill 90 balloons? Tank Pressure and Balloon Quantity Pressure in the helium cylinder (psi) Number of 9-inch balloons 100 30 150 ? 200? 250? 300?
According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons (PSI.)
Simply divide the number of balloons by the total PSI to arrive at this figure.
⇒990/300
⇒3.333333 psi each.
The no of the 90-inch balloon is found as;
⇒3.33333 × 90
⇒300
According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons.
Hence option D is correct.
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Please help solve for x..
Answer:
x = 1 or x = -1
Step-by-step explanation:
Given equation:
[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]
Factor out -1:
[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]
Divide both sides by -1:
[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]
Rearrange the terms:
[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]
[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]
Factor out the common term [tex](x^{98}-1)[/tex] :
[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]
Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):
[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]
Therefore, the solutions to the given equation are: x = 1 or x = -1
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If 5 hours at a computer terminal costs $25, what is the cost of 6 hours?
A. $30
B. $45
C. $150
D. $12
Answer:
30 dollars
Step-by-step explanation:
25/5 = 5 dollars per hour
so 6 hours would be 5 * 6 = 30 dollars
Answer:
It would be B
Step-by-step explanation:
First, we need to find out the unit rate
5/25=1/5
Therefore, that means in one hour the cost would be $5
Since you are going from one hour to 6 hours you need to multiply both numbers by 6
Since 5x6=30, it would be 30$ :)
Bearing a to b is 280 what is bearing b to A
Answer:
please see photo attached for detailed analysis.
Estimate the Value of 196/0.499
Answer:
The value of the expression will be "392.79".
Step-by-step explanation:
~ The technique of dividing a quantities into equivalent portions as well as determining however many equal components may be formed, is determined as a division.
~ It is denoted by "/".
According to the equation, the expression is:
→ 196/0.499
By applying the division, we get
→ 392.79
Answer:
392
Explanation:
Note that we are estimating, not finding the actual value. 0.499 is very close to 0.5, so to estimate this expression, we can do 196 ÷ 0.5. Dividing a number by 0.5 is the same as doubling it, so this can also be seen as
196 · 2, which is 392.
Hope this helps !! :D
The actual answer is the other one, but again, you're finding an estimate!
(c) The result of a number, when increased by 40%, is 2.1. Find the number. ( c ) The result of a number , when increased by 40 % , is 2.1 . Find the number .
Answer:
1.5 is the number.
Explanation:
Let the number be 'n', this is 100% - original number.
When increased by 40%, 100% + 40% = 140%.
140% × n = 2.1
1.4n = 2.1
n = 2.1/1.4
n = 1.5
Hence, the original number is 1.5.
What is the measure of the unknown angle?
straight angle divided into a one hundred thirty two degree angle and an unknown angle
48°
49°
51°
53°
A(-5, 2)
-10-8-6-4-2
10
↑リ
8
64
2
2
4.
6
-8
-10
B(1,6)
2
4
6 8 10
D(3,-10)
C(9,-6)
What is the area of rectangle ABCD?
O 43 units²
52 units²
O104 units²
O208 units²
The area of ABCD is 104 units²
What is area of rectangle?The area of rectangle is the product of its length to its breadth.
i.e., Area of rectangle= length * breadth
As, ABCD is in the shape of rectangle.
Using distance formula,
AB = √(1-(-5)² + (6-2)²
AB = √36+16
AB = √52
AB= 2√13
BC= √(9-1)² + (-6-6)²
BC= √64+144
BC =√208
BC= 4√13
Now, area of rectangle
=length * breadth
= 2√13 * 4√13
= 8*13
=104 units²
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