Answer:
x = 1
Step-by-step explanation:
Given
x + 2[tex]\sqrt{x}[/tex] - 3 = 0 ( subtract x - 3 from both sides )
2[tex]\sqrt{x}[/tex] = 3 - x ( square both sides )
4x = (3 - x)² ← expand using FOIL
4x = 9 - 6x + x² ( subtract 4x from both sides )
0 = x² - 10x + 9 ← in standard form
0 = (x - 1)(x - 9) ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 9 = 0 ⇒ x = 9
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are solutions.
x = 1 : 1 + 2[tex]\sqrt{1}[/tex] - 3 = 1 + 2 - 3 = 0 → x = 1 is a solution
x = 9 : 9 + 2[tex]\sqrt{9}[/tex] - 3 = 9 + 6 - 3 = 12 ≠ 0
x = 9 is an extraneous solution while x = 1 is a solution
1. Paulina wants to find the width, AB, of a river. She walks along the edge of the river 200 ft and marks point C. Then she walks 60 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown. (a) Can Paulina conclude that ΔABC and ΔEDC are similar? Why or why not? (b) Suppose DE = 40 ft. Calculate the width of the river, AB. Show all your work and round answer to the nearest tenth. Answer
Answer:
Step-by-step explanation:
a). In ΔABC and ΔEDC,
Since, AB and DE are parallel and AE is a transversal,
Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]
m∠D = m∠B = 90°
ΔABC ~ ΔEDC [By AA property of similarity of two triangles]
b). Therefore, by the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]
[tex]\frac{60}{200}=\frac{40}{AB}[/tex]
AB = [tex]\frac{40\times 200}{60}[/tex]
= 133.33
≈ 133.3 ft
what is 5 divided by 20.9
Answer:
0.23923444976
In math class, Jose earns 10 points for each A in his homework. If he already has 50 points, how many A’s does he need to get 120 points?
Answer jose needs to get 7 more A's because 5+7=12 so if 50+70=120 then he will need to get 7 more a's hope this helps :)
Step-by-step explanation:
Answer:
He needs 7 A's.
Step-by-step explanation:
The pictures.
Hope this helps!!! :)
4x + 7 + 4
I need helppp pls
Answer:
4x+11
Step-by-step explanation:
you have to add the like terms,in this case the like terms are 7 and 4.4x isn't a like term cause it has a variable.
so you just have to add 7+4
4x+11
I hope this helps
Step-by-step explanation:
hope this may help you tq
Simplify x + (7+14x)
Answer:
15x + 7
Step-by-step explanation:
x + (7 + 14x)
x + 7 + 14x
15x + 7
Answer:
15x + 7
Step-by-step explanation:
Remove parenthesis:
x + 7 + 14x
Combine like terms:
14x + x = 15x
Add the seven:
15x + 7
Hope this helped.
Can you please help me!!!!!
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that:
She plans to drive 400 miles.
She has at most $210 to spend.
Use the drop-down menu below to write an inequality representing dd, the total number of days Claire can rent the car while staying within her budget.
The required inequality that expresses the given condition is 36 + 29x ≤ 210.
Given that,
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that she plans to drive 400 miles. she has at most $210 to spend.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of days be x,
Total cost to drive 400 miles = 400(0.09) = $36.
According to the question,
36 + 29x ≤ 210
Thus, the required inequality that expresses the given condition is 36 + 29x ≤ 210.
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The volume of the triangular prism is 54 cubic units.
What is the value of x?
O 3
O 5
7
09
3x
Answer:
3
Step-by-step explanation:
The value of x is 3 if the volume of the triangular prism is 54 cubic units.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that volume of the triangular prism is 54 cubic units.
We have to find the value of x
The volume of the prism with triangular base is 54 unit³.
The base is a triangle with,
base = 4 units
height = x units
height of the prism = 3x
V= 6x²
54= 6x²
Divide both sides by 6
x² = 9
x=3
Hence, the value of x is 3 if the volume of the triangular prism is 54 cubic units.
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The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 49 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 89% confidence interval for the mean gas mileage for this car model.
Answer:
The answer is "(27.030,29.770)"
Step-by-step explanation:
[tex](\bar{x}) = 28.4[/tex]
[tex](n)= 49[/tex]
[tex](\sigma) = 6[/tex]
[tex](CI) = \bar{x}\pm z^*_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}[/tex]
[tex]z^*_{\frac{\alpha}{2}}\ for \ 89\%\ confidence = 1.598 \\\\\text{Using z table }\\\\ NORM.S.INV(1-\frac{(1-0.89)}{2})[/tex]
[tex]CI = 28.4 \pm 1.598 \times \frac{6}{\sqrt{49}}=(27.030,29.770)[/tex]
not sure how to solve
Help! ASAP. The question is in the attachment below
Answer:
Step-by-step explanation:
The most obvious answer is the line y = 1.
Help pls ?? I really don’t know what to do
Answer:
The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1
Step-by-step explanation:
all you have to do is replace the x in "G" with the "F" function
F(x) = x+4 and G(x) = x^3-1
===========================================================
Explanation:
Let's try choice A to see if it works or not
G(x) = (x+4)^3
G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)
G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1
G( F(x) ) = (x+3)^3
This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.
------------
Let's try choice B
G(x) = x+4
G( F(x) ) = F(x)+4
G( F(x) ) = x^3-1 + 4
G( F(x) ) = x^3 + 3
Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.
--------------
Now choice C
G(x) = x^3 - 1
G( F(x) ) = ( F(x) )^3 - 1
G( F(x) ) = (x+4)^3 - 1
We found the final answer.
I need help please Brainly fam
Answer:
The third one
Step-by-step explanation:
Just took the quiz
A rectangle has side lengths 2x + 3 and 5x - 2.
Write an expression without brackets for the area of the rectangle
Answer:
10x² + 11x - 6
Step-by-step explanation:
The area (A) is the product of the sides, that is
A = (2x + 3)(5x - 2) ← expand using FOIL
= 10x² - 4x + 15x - 6 ← collect like terms
= 10x² + 11x - 6
Which Venn Diagram is NOT correct?
Help pls will give brainliest
Answer:
195.06
Step-by-step explanation:
area of circle = πr^2 = π8^2 = 64π
area of triangle = 1/2 x 4 x 3 = 6
area of shape = 64π-6 = 195.061929 = 195.06
What is the area for the circle?
Answer:
108 squared centimeters
Step-by-step explanation:
Let's exchange π for 3:
area = πr^2
= 3r^2
Now, as you can see, the radius of this circle is 6. Let's plug in the value of r:
area = 3r^2
= 3 · 6^2
Simplify 6^2:
area = 3 · 6^2
= 3 · 36
Multiply 3 by 36:
area = 3 · 36
area = 108
108 squared centimeters
Menos 10 * 12 * -4 + 40 * -2 * 6 - 2 por favor
Answer:
-2
Step-by-step explanation:
-10 x 12 x -4 + 40 x -2 x 6 - 2
-120 x -4 - 80 x 6 - 2
480 - 480 - 2
0 - 2
-2
Does 8in to 1ft reduce it or enlarge it
Answer:
enlarge it
Step-by-step explanation:
I ft = 12 inches
Thus 8 in → 12 in makes the transformation larger.
Thus going from 8 in to 12 in is an enlargement
On what sum of money will the compound interest for 2 years at 8% p.a. will be ₹7448?
Answer:
Rs.6420
Step-by-step explanation:
we know that A=P(1+r/100)
7488=P(1+8/100)2
7488*10000/108*108=P
P=Rs.6420
Answer:
Principal=Rs.45000 ; And Amount=Rs.52488.
Step-by-step explanation:
For finding Principal i used the formula:[ x(1+8/100)^2-x] =C.I ( where x = P)
And for Amount : Sum of principal and interest.
Hope so, you liked my solution.
Find the equations of line in y = mx + b form...
a) Passes through the points (7, 9) and (2, -2)
Answer:
y = 11/5x - 32/5
Step-by-step explanation:
y2 - y1 / x2 - x1
-2 - 9 / 2 - 7
-11 / -5
= 11/5
y = 11/5x + b
-2 = 11/5(2) + b
-2 = 22/5 + b
-32/5 = b
Select the reason why these triangles are
similar. If they are not, select "Not similar."
1
88°
3
2
88
6
A. AA
B. SAS
C. SSS
D. Not similar
Answer:
B. SAS
Step-by-step explanation:
Ratio of sides equal:
• 4/2= 6/3
So the 2 sides are congruent and also share same angle between.
• B. SAS is the similarity reason
Determining the Domain and Range from a Graph
Determine the domain and range of the given function.
The domain is
ty
4
The range is
2
-4
-2
4
Into
Answer:
Domain is all real numbers, and range is all numbers greater than or equal to -2. If thee was anything you didn't understand let me know.
Step-by-step explanation:
The domain is what x values work, or it may be better to say the horizontal axis. is there any number you cannot use? if you cannot tell, this is a parabola, like x^2. Is there any number you cannot plug into x^2. The answer is no, the domain for all parabolic functions is all real numbers.
The range you really want to look at visually here. Range is y values you can get, or values on the vertical axis. I would also compare it to x^2 again. You should know you can make it as high as you want, here is the same. but at -2, there is no point below that. so the range is -2 and up
The other options are just specific numbers. you can disprove those by choosing a number not on their lists. For the domain literally any other number. For range any number not on the list greater than -2
three less than twice the square of a number is 47.
Answer:
5
Step-by-step explanation:
[tex]5^{2}[/tex] = 25
25 * 2 = 50
50 - 3 = 47
Hope that this helps!
Answer:
Step-by-step explanation:
let the number be x
Square of a number: x²
Twice the square of a number = 2*x² = 2x²
Three less than twice the square of a number = 2x² - 3
2x² - 3 = 47 {Add 3 to both sides}
2x² = 47 + 3
2x² = 50 {Divide both sides by 2}
x² = 50/2
x² = 25 Take square root
x = √25
x = 5
2.
8 + 4ab - 5b
Number of terms:
Coefficients:
Constant terms:
Answer:
8= coefficients.
4ab=constant term
5b=number of terms
Step-by-step explanation:
when terms are being added and substrated in algebra expression, we can sometimes simplify the expression to produce an expression with fewer terms
LET ME KNOW IF IT HELPS
Write all the possible two-digit numbers which can be formed using the digits 0,3,5
Answer:
i) where the digits can repeat
1. 30
2. 50
3. 33
4. 55
5. 35
6. 53
ii) where the digits cannot be repeated
1. 30
2. 50
3. 35
4. 53
help please, i'll give brainliest
The cost of a pen is three times and Rs 4 more than the cost of a pencil. If three pencils and two pens cost Rs 71, find the cost of each item.
Answer:
1.
= Here,
cost of pen = 3+4 ( x ) = 7x
costs of two pen = 7x
cost of three pencils = 71 - 7x = 64x
cost of 1 pencil = 64/3
= 21.333334
c
Simplify xy-5x+y^2xy−5x+y 2 if x = -3 and y = 5.
The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex] gives - 335.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]xy-5x+y^2xy-5x+y ^2[/tex]
Substitute x = -3 and y = 5.
[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]
= -15 + 15 - 375 + 15 + 25
= -335
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How do I answer the questions in 4 c
Answer:
Step-by-step explanation:
i. 5/12
ii. 1/8
iii. 11/24
iiii. 7/8
