Given:
The equation is:
[tex]\sqrt{x+7}+5=x[/tex]
To find:
Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.
Solution:
We have,
[tex]\sqrt{x+7}+5=x[/tex]
Subtract 5 from both sides.
[tex]\sqrt{x+7}=x-5[/tex]
Taking square on both sides, we get
[tex]x+7=(x-5)^2[/tex]
[tex]x+7=x^2-10x+25[/tex]
[tex]0=x^2-10x+25-x-7[/tex]
[tex]0=x^2-11x+18[/tex]
Splitting the middle term, we get
[tex]x^2-2x-9x+18=0[/tex]
[tex]x(x-2)-9(x-2)=0[/tex]
[tex](x-2)(x-9)=0[/tex]
[tex]x=2,9[/tex]
Now, substitute [tex]x=2[/tex] in the given equation.
[tex]\sqrt{2+7}+5=2[/tex]
[tex]\sqrt{9}+5=2[/tex]
[tex]3+5=2[/tex]
[tex]8=2[/tex]
This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.
Substitute [tex]x=9[/tex] in the given equation.
[tex]\sqrt{9+7}+5=9[/tex]
[tex]\sqrt{16}+5=9[/tex]
[tex]4+5=9[/tex]
[tex]9=9[/tex]
This statement is true. So, 9 is a solution of given equation.
Therefore, 2 is an extraneous solution and 9 is a solution of given equation.
What is the slope of the line passing through the points (-5, -4) and (-1, 6)?
Step-by-step explanation:
using the formula (y2-y1)/(x2-x1)we plug the numbers In the slop formula (6--4)/(-1--5)= 10/4
Answer:
Step-by-step explanation:
(x1,y1)= (-5,-4)
(x2,y2)=(-1,6)
Distance=√(x2-x1)²+(y2-y1)²
=(-1-5)²+(6-4)²
=(-6)²+(10)²
=36+100
=136 answer,,
therefore, the slope of the line is 136unit
Diego has a standard 52 card playing deck, which includes
13 heart cards, 13 spade cards, 13 diamond cards, and 13
club cards. If he draws one card at random, what is the
probability that the card will be a heart?
Answer:
13/52
Step-by-step explanation:
5. The property depicted in the expression 2/( 3) ×(1/3+ 4/5)=(2/3 × 1/3)+(2/3 × 4/5) is *
associative property of addition
associative property of multiplication
distributive property of multiplication
closure property of multiplication
Answer:
distributive property of multiplication over addition
Step-by-step explanation:
a(b + c) = ab + ac
The a to the left of the parentheses multiplies both numbers inside the parentheses. The you add the products.
This is the distributive property of multiplication over addition.
2/3 × (1/3 + 4/5) = (2/3 × 1/3) + (2/3 × 4/5)
The 2/3 to the left of the parentheses multiplies both numbers inside the parentheses. The you add the products.
This is the distributive property of multiplication over addition.
A gum ball machine has 6 red gum balls, 3 green gum balls, and 5 blue gum balls. What is the probability that the next gum ball that comes out will be red?
Answer:
Step-by-step explanation:
P(red gum ball)= 6/14=3/7
6/14 can be simplified to 3/7 by dividing by 2. 6/2=3. 14/2=7.
P(red gum ball)=3/7
Which of the following is equivalent to 5(4-m)-2(m+3)? *
don’t give me that link .
[tex]\longrightarrow{\green{Option\:1.\:(14\:-\:7m)}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]5 \: (4 - m) - 2 \: (m + 3) \\ \\ = 20 - 5m - 2m - 6[/tex]
Combining like terms, we have
[tex] = 20 - 6 - 5m - 2m \\ \\ = 14 - 7m[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
yes need help again im on my math exam review thing i.dk wut it tis also here are some extra points im feelin nice today btw dont jus answer for the points or put a site or ill report.
ᴍɪʟʟʏ~
Answer:
(-5) + 8 + (-5) = -2
Step-by-step explanation:
The first point is 5 points to the left of 0, or -5
Next, it goes right 8 units (+8) and lands on 3
THen it goes back 5 units (-5) and lands on -2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
help guys pls i beg u cannot do the math this so hard someone help ☺️☺️☺️☺️☺️☺️☺️☺️
Tell whether the triangle with the given side lengths is a right triangle. 36, 77, 85, true or false
Answer:
True the triangle is a right triangle.
Step-by-step explanation:
the Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex]
so,
[tex]85^{2} =7225\\77^{2} =5929\\36^{2} =1296\\5929+1296=7225[/tex]
a submarine starts out at 120 feet below sea level it dives another 175 feet and then rises 228 feet. what is the current depth of the submarine
Which inequality represents “six times a number is less than negative
6x >-39
4
6 + x>-39
6x < -39
4
6x5-393
4
Answer:
6x < - 39 3/4
Step-by-step explanation:
HELP PLEASE I WILL MARK BRAINLIEST
Answer:
i beleive its option number 1
Answer:
first graph
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Then g(x) = | x | - 4 is the graph of f(x) shifted down by 4 units
This is represented by the first graph on the left
Work out the base of a square with area,
A
= 64cm2.
Answer:
32
Step-by-step explanation:
because 64 divided by 2 is 32
State if triangles HAG and CAB are similar and why.
Please help me please I will really appreciate
Answer:
Step-by-step explanation:
If we draw this triangle with Q as the vertex angle (the one at the top of the triangle) then the 2 sides are congruent and this is an iosceles triangle. Because this is an isosceles triangle, then the 2 base angles, angle R and angle S are congruent. If Q measures 114 degrees, then angles R and S together have to add up to the difference between 180 and 114:
180 - 114 = 66
Divide that in half so R = S = 33 degrees each
What is the volume of the prism?
Answer:
[tex]volume \: of \: the \: prism = 4 \frac{1}{2} \times 2 \ \frac{1}{2} \times 6 \\ = \frac{9}{2} \times \frac{5}{2} \times 6 \\ = 67.5 {cm}^{3} [/tex]
hi, i know this is basic math and stuff but I still need some help
Answer:
the answer is :
20 for the first figure
12 for the second figure
30 for the last figure
Answers:
Perimeter = 22 cmPerimeter = 22 cmPerimeter = 30 cm==============================================
Explanation:
The perimeter is the total distance around the outer edge of the figure. It's the total amount of fence you need to enclose the region.
So we simply add up all the side lengths. Refer to the diagram to see any missing sides that aren't labeled (shown in blue).
For instance, the perimeter for problem 1 is 5+2+2.5+4+2.5+6 = 22 cm. Problems 2 and 3 are handled the same way.
It's not a typo that the perimeters of problems 1 and 2 are the same value. This is because both figures can be surrounded by a rectangle that is 6 cm across and 5 cm tall. The perimeter of the surrounding rectangle is exactly the same as the perimeter of the inner fenced region. We're effectively just moving fence around but not changing the perimeter.
570
1. Volume of a pyramid: 192 ftº: Volume of a rectangular prism:
2. Volume of a pyramid:
Volume of a rectangular prism: 729m
3. Volume of a cylinder: 285 cm: Volume of a cone:
4. Volume of a sphere:
Volume of a cylinder: 600cm
5. Volume of a cone: 50 m: Volume of a cylinder:
Answer:
576 FT^3
243 m^3
95 cm^3
400 cm^3
150 m^3
Step-by-step explanation:
Volume of a pyramid = 1/3 x ( length base x height)
Volume of a prism= ( length base x height)
1. prism = 192 x 3 = 576 FT^3
2. prism = 729 / 3 = 243 ft^3
volume of a cylinder = nr^2h
Volume of a cone = 1/3(nr^2h)
3. cone = 285/3 = 95
5. cylinder = 50 x 3 = 150
4. sphere = 600 / 1.5 = 400
The length of a box is 6 inches, the width is 4 inches and the height is 2/8 inches. What is the volume of the box?
Answer:
6 cubic inches
Step-by-step explanation:
To find the volume of a box you do Length * Width * Height
So we can do:
6*4*2/8
=24*2/8
=6
The volume of the box is 6 cubic inches
in a group of 120 students,90 students study mathematics and 72 study science. if 10 of the student does not study any subject
1)find the no.of students who study atleast 1 subject
2)number of students studying both subjects
3)how many students will study mathematics only?
4)how many students will study science only?
Answer:
Step-by-step explanation:
Total students = 120
Number of students studying Mathematics P(A) = 90
Number of students studying Science P(B) = 72
Number of students who doesn't study both subjects P(AUB)'= 10
1) Number of students studying atleast on subject = 120 -10 = 110
2) Number of students studying both math and science = (90 +72) -110
= 162 -110 = 52
3) Number of students studying only mathematics = 90 -52 = 38
4) Number of students studying only science = 72 -52 = 20
NEED HELP ASAPPP PLZ JUST NEED THE ANSWER NOT THE WORK THANK YOU.
Answer:
C. 2^8 • 2^(2/10) • 2^(4/100)
which expressions have value between 1 and 2? choose all that apply.
Answer:
its the first, 3rd, and 5th option
Step-by-step explanation:
Jacqui likes to travel to the beach on weekends. She starts at her house, drives d miles, and then spends t hours walking the remaining w miles to get to the beach. Jacqui drives three times as long as she walks during the trip. The equation below represents Jacqui's average speed, a, in miles per hour, when traveling to the beach. a=d+w/3t+t What is the meaning of 3t + t3t+t in the equation above? -The total time that Jacqui spends traveling to the beach -The time that Jacqui spends driving to the beach -The total distance that Jacqui travels to the beach -Jacqui's maximum speed during her trip Jacqui's average speed during one trip to the beach was 3636 miles per hour. If Jacqui drove 70 miles and the entire trip to the beach took her 22 hours, how many miles did she walk to get to the beach?
Answer:
The answer is below
Step-by-step explanation:
1) Average speed is the ratio of the total distance travelled to the total time taken. Hence it is given by:
Average speed = total distance / total time
Total distance = d miles + w miles
Jacqui drives three times as long as she walks during the trip, hence:
time spent driving = 3t
Total time = 3t + t
Average speed = total distance / total time
a = (d + w) / (3t + t)
2) (3t + t) represents the total time that Jacqui spends traveling to the beach.
3) Given that a = 36 miles per hour, total time = 2 hours
a = total distance / total time
36 miles per hour = total distance / 2 hours
total distance = 72 miles
Total distance = distance walk + distance drove
72 = distance walk + 70
Distance walk = 2 miles
Which input value produces the same output value for the two functions on the graph
X = 1
Because where the two lines intersect, they have the same x value, one
Answer:
x = 1
Step-by-step explanation:
Look at the graph to see where the lines intersect.
f(1) = 1
g(1) = 1
When x = 1, the output value of both functions is 1.
Answer: x = 1
Dada a função fx=0,15.X+900 , determine a) f(80) b) f(120) c) f(200) d) f(56)
Answer:
See answers below
Step-by-step explanation:
Given the function:
f(x) = 0.15x + 900
a) f(80) = 0.15(80) + 900
f(80) = 12 + 900
f(80) = 912
b) f(120) = 0.15(120) + 900
f(120) = 18 + 900
f(120) = 918
c) f(200) = 0.15(200) + 900
f(200) = 30 + 900
f(200) = 930
d) f(56) = 0.15(56) + 900
f(56) = 8.4 + 900
f(56) = 908.4
¿¿ Cuanto es "6 + -7 - (-8) + 4 – 2" ??
Answer:
9
Step-by-step explanation:
Do it left from right.
[6+-7]-(-8)+4-2
[-1-(-8)]+4-2=[-1+8]+4-2
[7+4]-2
11-2
9
I don't know Spanish/what laugnange you speak sorry.
Consider the equation and its solution.
— 15(x-O) = 25
— 15х+ 30 = 25
— 15х = -5
What number should be in the empty box?
-30
-2
Оооо
30
On a coordinate plane, 4 lines are shown. Line L M goes through (negative 5, negative 3) and (0, 3). Line N O goes through (negative 6, negative 5) and (0, 0). Line J K goes through (negative 6, 1) and (0, negative 4). Line P Q goes through (negative 5, 4) and (0, negative 2).
Which line is perpendicular to a line that has a slope of Negative five-sixths?
Answer:
The slope of line LM is perpendicular to the given line.
Step-by-step explanation:
L (- 5, - 3), M (0, 3)
N (- 6, - 5) , O (0, 0)
J (- 6, 1) , K (0, - 4)
Slope of given line = -5/6
Slope of perpendicular line = 6/5
Slope of line LM
[tex]\frac{3 + 3}{0 + 5}=\frac{6}{5}[/tex]
Slope of line NO
[tex]\frac{0+5}{0+6}=\frac{5}{6}[/tex]
Slope of line JK
[tex]\frac{-4-1}{0+6}=\frac{-5}{6}[/tex]
Answer: LM is the correct answer
Step-by-step explanation: Just took the test
please help. its for an assignment that is due today.
•Sequences and functions
( 10 points )
Please help me loves with the answer and understanding
•Please actually help me out I want to better understand this
•trolls will be reported
if the sub total is 5.00 and tax is 5% how much is tax
Answer:
$0.25
Step-by-step explanation:
So total of 5.25 after tax Sorry if i am wrong am pretty sure this is correct.