Answer:
x = -34
Step-by-step explanation:
-3x + 2x -34 = 0
sum the x
-3x + 2x = -x
replace -x in the equation
-x -34 = 0
move -34 to other side
-x = 34
divide the two sides by -1 to get x value
x = -34
now replace x value in the equation:
-3(-34) + 2(-34) -34 =
102 -68 -34 =
102 -102 = 0
Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²
The choice which is equivalent is [tex]6x^2\sqrt{3}[/tex] option B
How to determine the valueWe have that;
[tex]\sqrt{6x^2} * \sqrt{18x^2}[/tex] where [tex]x\geq 0[/tex]
First, we factorize the square root
= [tex]\sqrt{2 * 3 * x^2 } . \sqrt{3 * 3 * 2 * x^2}[/tex]
Find the common factors
= [tex]2 * 3 x^2\sqrt{3}[/tex]
= [tex]6x^2\sqrt{3}[/tex]
Thus, the choice which is equivalent is [tex]6x^2\sqrt{3}[/tex] option B
The complete question is;
Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²
a. [tex]6\sqrt{3x}[/tex]
b. [tex]6x^2\sqrt{3}[/tex]
c. [tex]6\sqrt{18x}[/tex]
d. [tex]\sqrt{108x^2}[/tex]
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Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
the expression simplified is:
[tex]12x^3 - 25x^2 + 9[/tex]
How to simplify the given expression?
Here we have the expression:
[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]
We just need to distribute the product, we will get:
[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]
Now we just need to group terms with the same exponent of x:
[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]
That is the expression simplified
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Geometry question please help!
Answer:
4
Step-by-step explanation:
Since,
The width of the Longer gear is 7, and the smaller gear has a width of 3..
7-3 = 4
Hope it helps...
Marking me as Brainliest would help me... :(
the center of a circle is on the line y=2x and the line x=1 is tangent to the circle at (1,6).find the center and the radius
The radius and the center of the circle are 4 units and (1,2), respectively
How to determine the center and the radius?The center of the circle is on
y = 2x and x = 1
Substitute x = 1 in y = 2x
y = 2 * 1
Evaluate
y = 2
This means that the center is
Center = (1, 2)
Also, we have the point of tangency to be:
(x, y) = (1, 6)
This point and the center have the same x-coordinate.
So, the distance between this point and the center is
d = 6 - 2
d = 4
This represents the radius
Hence, the radius and the center of the circle are 4 units and (1,2), respectively
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A ladder is leaning against a building as shown in the
diagram.
How many feet up the side of the building is the top of
the ladder?
ft
10 feet
6 feet
The length of ladder is 30 ft.
How can the feet that made up the side of the building is the top of the ladder be known ?The formula below can be used in solving the problem
Tan (∅)= [tex]\frac{opposite}{adajacent}[/tex]
∅=70°
opposite = BC
Adjacent = 12 ft
70°= opposite/ 12
opposite= 32.96 ft
Therefore, The length of ladder is 30 ft.
NOTE; Since the actual diagram can not be found i solved another on on the same topic
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CHECK COMPLETE QUESTION BELOW:
Consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12ft from the building. how long is the ladder? (to the nearest ft)
a. 25ft
b. 30ft
c. 35ft
d. 40ft
what is 73 division 84,649
73 division 84, 649 would give 8. 64 × 10^-4
How to determine the valueIn order to determine the value of the division, we have
= [tex]\frac{73}{84649}[/tex]
Using the calculator, put the values in
We would have
= 8. 64 × 10^-4
Thus, 73 division 84, 649 would give 8. 64 × 10^-4
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For f(x) = 2x + 1 and g(x) = x² - 7, find (f+ g)(x).
Answer:
(f + g)(x) = x² + 2x - 6
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7 ← collect like terms
= x² + 2x - 6 ← in standard form
Evaluate functions from their graph Problem g(3) =
See attached for the correct answer!
The notation g (3), left parenthesis, 3 refers to the output of the function when the input is x=. If the point (3, b) is on the graph, then g (3) =b.
We should look for the point on the graph whose x- coordinate is 3 is the point )3, 4).
The point on the graph whose x-coordinate is 3 is the point (3,4).
Therefore, g (3) = 4
The value of g(3) is g(3) = 4
How to evaluate the function?The function value is given as:
g(x)
The notation g(3) implies that:
We determine the value of g(x) when x = 3
From the graph, the function has a point at (3,4)
This means that:
When x = 3, g(x) = 4
i.e. g(3) = 4
Hence, the value of g(3) is g(3) = 4
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Solve the inequality for x.
5x-39-3(6-4x)
Simplify your answer as much as possible.
Answer:
= 5x-39-18-12x
=5x-12x-39-18
=-7x-57
(c) Use a calculator to verify that Σ(x) = 64, Σ(x2) = 1118, Σ(y) = 628, Σ(y2) = 87,982, and Σ(x y) = 9,627.
Compute r. (Enter a number. Round your answer to three decimal places.)
The correlation based on the computation is 0.97.
How to compute the value?It should be noted that the question is that we should simply calculate the correlation which is r.
The correlation will be:
= Σ(x y) / (Σ(x²) × Σ(y²)
= 9627/✓(1118 × 87982)
= 9627 ✓98363876
= 9627/9917.86
= 0.97
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D
C
63. If AD 20 centimeters, DC= 15 centimeters,
BC=7 centimeters, and AB = 24 centimeters,
what is the area of quadrilateral ABCD?
A. 66 sq cm
B.
B
117 sq cm
C. 234 sq cm
D.
468 sq cm
The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)
What is the area of the quadrilateral?
Herein we have a description of an irregular quadrilateral, whose area must be determined by adding the areas of minor quadrilaterals and triangles that are part of it. The area is now determined:
A = 0.5 · (24 cm) · (7 cm) + 0.5 · (15 cm) · (20 cm)
A = 234 cm²
The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)
Remark
The picture with the quadrilateral is missing and is included as attachment.
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1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.
The number of female contestants who signed up to compete is; 43.
What is the number of female contestants?Let number of females = x
Let number of males = y.
Hence, it follows from the task content that;
x+y = 50
x-y = 36.
Hence, by adding both equations together in a bid to determine the number of females; we have;
2x = 86
x = 43.
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.....................
Answer: 5020
Step-by-step explanation:
10^3= 1000
1000*5.02=5020
The wheel of the average bicycle is 28 inches in diameter. How many feet will be covered in 9
turns of the wheel?
Answer:
Approximately 66 feet
Step-by-step explanation:
Given d = 28 inFind the circumference:
C = πd = 3.14*28 = 87.92 inFind the distance covered by 9 turns:
9C = 9*87.92 = 791.28 inConvert inches to feet:
1 foot = 12 in791.28 in = 791.28/12 ft = 65.94 ft ≈ 66 ftFind the area of a triangle with legs that are: 16 m, 12 m, and 8 m.
Answer: 46.48 m²
Step-by-step explanation:
this question was answered already, go search it up
Which of the following is most likely the next step in the series
Answer:
A
Step-by-step explanation:
The pattern is quadrilateral (4-gon), pentagon (5-gon), and hexagon (6-gon). Therefore the next figure would be a heptagon (7-gon).
An equestrian club orders magazine subscriptions for new members.
Last year they had 32 new members and spent $624 on subscriptions.
Use the equation 32m = 624 to find the cost of each subscription.
Enter your answer in the box.
Answer:
$19.50
Step-by-step explanation:
Dividing both sides by 32, we get $19.50.
which of the following statements is true about the solution of the system? 2x-y=8 and y=2x-3
Answer:
no roots.
Step-by-step explanation:
[tex]\left \{ {{2x-y=8} \atop {y=2x-3}} \right. \ = > \ \left \{ {{2x-y=8} \atop {2x-y=3}} \right. \ = > \ no \ solution.[/tex]
3. Consider the equation 2x² + 4y² + 8x - 16y + F = 0. Find all values of F such that the graph of the equation is a) an ellipse b) a point - ellipse
The equation 2•x² + 4•y² + 8•x - 16•y + F = 0, at a value of F is the graph of an ellipse when we have;
a. A value of F that results in the equation of an ellipse is; F = 23
b. A point on the ellipse is ((-2), 2.5)
Which method can be used to find the value of F that gives the graph of an ellipse?The equation of an ellipse can be presented as follows;
[tex] \frac{(x - h) ^{2} }{ {a}^{2} } + \frac{(y - k) ^{2} }{ {b}^{2} } = 1[/tex]
The given equation can be presented as follows;
2•x² + 4•y² + 8•x - 16•y + F = 0
Collecting like terms, gives;
2•(x² + 4•x) + 4•y² - 16•y + F = 0
Adding a constant value to both sides, we get;
2•(x² + 4•x + 4) + 4•y² - 16•y + 16 + F = 24
2•(x + 2)•(x + 2) + (2•y - 4)•(2•y - 4) + F = 24
2•(x + 2)² + 4•(y - 2)² + F = 24
2•(x + 2)² + 4•(y - 2)² + F - 23 = 24 - 23 = 1
When F = 23, we have;
2•(x + 2)² + 4•(y - 2)² + 23 - 23 = 1
2•(x + 2)² + 4•(y - 2)² = 1Which gives;
[tex] \mathbf{\frac{(x + 2) ^{2} }{ \left( {\frac{1}{ \sqrt{2} }} \right)^{2}} + \frac{(y - 2) ^{2} }{ \left( {\frac{1}{ 2} } \right)^{2}} } = 1[/tex]
Where;
a = 1/(√2)b = 1/2b) A point on the ellipse can be found as follows;
2•(x + 2)² + 4•(y - 2)² = 1When x = -2
2•((-2) + 2)² + 4•(y - 2)² = 1
0 + 4•(y - 2)² = 1
y - 2 = √(1/4) = 1/2
y = 2 + 1/2 = 2.5A point on the ellipse is therefore;
((-2) , 2.5)When y = 2
2•(x + 2)² + 4•(2 - 2)² = 1
2•(x + 2)² + 0 = 1
2•(x + 2)² = 1
(x + 2)² = 1/2
x + 2 = √(1/2)
x = √(1/2) - 2
Another point on the ellipse is therefore;
((√(1/2) - 2), 0)
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Select the solution to the following system of equations:
4x + y = 6
2x - 3y = -4
The solution to the given system of linear equations is x = 1, y = 2. That is (1, 2)
Simultaneous linear equationsFrom the question, we are to solve the given system of equations
The given system of equations is
4x + y = 6 -----------(1)
2x - 3y = -4 -----------(2)
From the equation (1)
4x + y = 6
y = 6 - 4x ----------(3)
Substitute the value of y into equation (2)
2x - 3y = -4
2x -3(6 - 4x) = -4
2x -18 +12x = -4
2x + 12x = -4 + 18
14x = 14
x = 14/14
x = 1
Substitute the value of x into equation (3)
y = 6 - 4x
y = 6 - 4(1)
y = 6 - 4
y = 2
Hence, the solution to the given system of linear equations is x = 1, y = 2. That is (1, 2)
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Find the surface area of this cone.
60π m2
20π m2
36π m2
54π m2
The surface area of a cone with radius of 4 m and slant height of 5 m is 36π m²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of a cone with radius (r) and slant height (l) is:
S.A = πr(r + l)
Given that r = 4, l = 5, hence:
S.A = π(4)(4 + 5) = 36π m²
The surface area of a cone with radius of 4 m and slant height of 5 m is 36π m²
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Answer:
36π m2
Step-by-step explanation:
James has $20 in his wallet and makes $10 per hour. Kelly has $50 in her wallet but only makes $8 per hour.
How many hours of work will it take for these two people to have the same amount of money?
Answer:
At 15 hours of work they will be equal.
Step-by-step explanation:
James: y = 10x + 20
Kelly: y = 8X + 50
Set them equal to each other and solve
10x + 20 = 8x + 50 Subtract 8x from both sides of the equation
2x + 20 = 50 Subtract 20 from both sides of the equation
2x = 30 Divide both sides by 2
x =15
If you spend $50 (including shipping) at an online store, you recieve a $10 gift card. You want to purchase CDs that cost $12 each. If shipping cost $5, write and solve an inequality to find the number of Cds you must to receive the giftcard.
Four CDs must be bought to receive a gift card from an online store.
How to determine the least number of CDs to be bought to receive a gift card
The total costs are equal to the sum of the shipping cost and the total related to the number of acquired CDs (n). The number of gift cards (m) is equal to the total costs divided by minimum spent money, that is, $ 50. We need to solve the following inequation to find the minimum quantity of CDs:
(12 · n + 5)/50 > 1
12 · n + 5 > 50
12 · n > 45
n > 45/12
n > 3.75
Four CDs must be bought to receive a gift card from an online store.
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he cone below has a radius of 3 inches, a height of 4 inches, and a slant height of 5 inches.
What is the approximate lateral area of the cone? Use 3.14 for π and round to the nearest whole number.
38 in.2
47 in.2
75 in.2
94 in.2
The lateral area of the cone is calculated as: B. 47 in.².
How to Find the Lateral Area of a Cone?Lateral area = πrl
Given the following:
Slant height (l) = 5 inches
Radius (r) = 3 inches.
π = 3.14
Plug in the values
Lateral area = (3.14)(3)(5)
Lateral area ≈ 47 in.²
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A jar of tickets for a drawing contains 22 winning tickets and 63 non-winning tickets. What are the odds against winning in the drawing? please help
Answer: 22/85
Step-by-step explanation:
Answer:
22/85
Step-by-step explanation:
2) Put the following numbers in order from
greatest to least.
6.05, 6.007, 6.5, 6.25
Answer: 6.5, 6.25, 6.05, 6.007
Step-by-step explanation:
We need to look at each place value to see which one is the biggest. Since the units place is the same for all the numbers, let's look at the tenths place.
6.5, 6.25, 6.05, 6.007
Since 5 is the biggest number out of all that are underlined, 6.5 is the biggest one, and goes first.
2 is the second biggest number out of all that are underlined, so 6.25 goes second.
However, there are 2 numbers that have 0 in their tenths place, so we need to go one place value further: the hundredths place.
6.05, 6.007
Since 5 is bigger than 0, 6.05 goes third. 6.007 is the only number left, so it goes last.
Hence, the order is 6.5, 6.25, 6.05, 6.007
Convert the following equation into slope-intercept form.
7x+y = 7
y = -7x+?
Answer:
y = - 7x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
7x + y = 7 ( subtract 7x from both sides )
y = - 7x + 7 ← in slope- intercept form
use long division to convert 3/10 into decimals.
Answer:
3/10 as a decimal is expressed as 0.3.
I need help with this geometry question asap!
No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.
When are Two Lines Proven to be Parallel to each other?Two lines that are cut across by a transversal can be proven to be parallel to each other if:
The alternate interior angles along the transversal and on the two lines are congruent [alternate interior angles theorem].The alternate exterior angles along the transversal and on the two lines are congruent [alternate exterior angles theorem].The same-side interior angles along the transversal and on the two lines are supplementary [same-side interior angles theorem].The corresponding angles along the transversal and on the two lines are congruent [corresponding angles theorem].Thus, given the following information:
m∠2 = 115°
m∠15 = 115°
With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.
In summary, we can conclude that:
D. None of the options are correct.
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> Function g can be thought of as a translated (shifted) version of Y f(x) = x².
Using translation concepts, function g(x) is given as follows:
g(x) = x² - 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift down of 3 units of f(x) = x², hence:
g(x) = x² - 3.
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