Answer:
➩ [tex]x=2,-\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{4x^2}=x+2[/tex]
➨ We can also solve by completing both squares, however. Since we can pull out the square root.
[tex]\sqrt{4x^2}=|2x|[/tex] ➩ Define of Absolute Value/Square Root
➩ [tex]\sqrt{x^2}=|x|[/tex]
Thus, our new equation is ➩ [tex]|2x|=x+2[/tex]
To solve an absolute-value equation, let there be two conditions.
➨ Where x ≥ 0
[tex]2x=x+2\\[/tex]
Move x to another side
[tex]2x-x=2\\x=2[/tex]
➨ Where x < 0
[tex]-2x=x+2\\-2x-x=2\\-3x=2\\x=\frac{2}{-3}\\x=-\frac{2}{3}[/tex]
On average, cody runs 4 miles in 38 minutes. How fast should he plan to run a 10-mile race if he maintains this place.
A: 1 hour 3 minutes
B: 1 hour 16 minutes
C: 1 hour 35 minutes
D: 2 hours 30 minutes
Answer:
C
Step-by-step explanation:
10/4=2.5
2.5x38=95
95 minutes= 1 hour 35 minutes
As an estimation we are told £3 is €4. Convert £54.20 to euros.
Answer:
$40 in euros!
Step-by-step explanation:
(4+2k)⋅6+3k and cant solve it plz help
Answer:
Simplifying
(4 + 2k) * 6 + 3k = 0
Reorder the terms for easier multiplication:
6(4 + 2k) + 3k = 0
(4 * 6 + 2k * 6) + 3k = 0
(24 + 12k) + 3k = 0
Combine like terms: 12k + 3k = 15k
24 + 15k = 0
Solving
24 + 15k = 0
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-24' to each side of the equation.
24 + -24 + 15k = 0 + -24
Combine like terms: 24 + -24 = 0
0 + 15k = 0 + -24
15k = 0 + -24
Combine like terms: 0 + -24 = -24
15k = -24
Divide each side by '15'.
k = -1.6
Simplifying
k = -1.6
Step-by-step explanation:
NEED HELP NOW WILL GIVE BRAINLEIST!!!!!!b) Calculate the area of the red triangle to find the area of the garden. Show your work. (2 points)
Answer: 9 ab is the area of the garden.
No scale or dimensions are given, so
Estimating to get a practical, reasonable answer:
Using typical walkway widths to 6 ft, it is reasonable to calculate the area the red triangle to be 486 square feet
and the area of the garden to be about 4400 square feet, rounding up.
OR
Using a metric standard of 2 meters, The area of the red triangle would be 54m²
The area of the garden would be about 500m²
Step-by-step explanation:
The area of the red triangle is [tex]A = \frac{ab}{2}[/tex] That is assuming that it is a right triangle and side a is the altitude or height of the triangle and side b is the base.
The measurements of the triangle are approximately in the proportion of 3, 4, 5, a typical "Pythagorean Triple" right triangle.
Estimating from rough measurements of the triangle and the dimensions of the garden as shown, it appears that the area of the garden is about 18 times the area of the red triangle.
The area of the triangle is half the area of a rectangle with the same side lengths a & b, so 9 ab is a good estimate of the area of the garden.
If the walkways are the typical 6 foot width found in many public gardens, and the length side b is the about 6 of those widths, and side a is about 4.5 of those widths, we can estimate the altitude to be 27 and the base to be 36 (in the proportion 3:4).
Area of the triangle estimate: A = 36ft × 27ft /2 = 486 square feet
OR
Using a metric standard, estimate a 2 meter wide sidewalk, the area of the triangle can be reasonably calculated to be A = 9m × 12m /2 = 54 m²
The area of the garden would be 9 × 54 = 486m² rounded reasonably to 500m²
Answer: 5400
Step-by-step explanation:The area of the triangle is defined as the product of half the base and the height of the triangle. The area of the triangle = 1/2 x b x h It is given that the length of the sides are as A= 90 B=120 C=150.
So, The area of the triangle = 1/2 x b x h = b x h/2 = 120 x 90/2 = 10800/2 = 5400
Jeffery babysits for 4 dollars per hour, he also works as a math tutor for 7 dollars per hour. He is only allowed to work 13 hours total per week. He wants to make at least 65 dollars. Write a system of inequalities to represent this situation.
Given:
Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.
He is only allowed to work 13 hours total per week.
He wants to make at least 65 dollars.
To find:
The system of inequalities to represent this situation.
Solution:
Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.
He is only allowed to work 13 hours total per week. It means sum of x and y must be less than or equal to 13.
[tex]x+y\leq 13[/tex]
He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.
[tex]4x+7y\geq 65[/tex]
Number of hours can not be negative.
[tex]x\geq 0, y\geq 0[/tex].
Therefore, the required system of inequalities contains some equations, [tex]x+y\leq 13,4x+7y\geq 65[/tex] and [tex]x, y\geq 0[/tex].
Determine whether each equation is True or False. In case you find a "False" equation, explain why is False.
Answer:
(1) TRUE.
(2) FALSE.
(3) FALSE.
(4) TRUE.
(5) FALSE.
Step-by-step explanation:
(1) [tex]\sqrt{32} = 2^{\frac{5}{2} }[/tex]
[tex]2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}[/tex]
Thus, the equation is TRUE.
(2) [tex]16^{\frac{3}{8} } = 8^2[/tex]
[tex]16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64[/tex]
Thus, the equation is FALSE.
(3) [tex]4^{\frac{1}{2} } = \sqrt[4]{64}[/tex]
[tex]4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}[/tex]
Thus, the equation is FALSE.
(4) [tex]2^8 = (\sqrt[3]{16} )^6[/tex]
[tex]2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256[/tex]
Thus, the equation is TRUE.
(5) [tex](\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\[/tex]
[tex]8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4[/tex]
Thus, the equation is FALSE.
plzzz help me with this
Answer:
Please find attached the required flow chart proof created using Microsoft Visio
Step-by-step explanation:
The given parameters are;
[tex]\overline {BD}[/tex] bisects ∠ADC and ∠ABC
Required to proof that ΔABD ≅ ΔCBD
The two column proof is given as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline {BD}[/tex] bisects ∠ADC [tex]{}[/tex] Given
∠ADB ≅ ∠CDB [tex]{}[/tex] Definition of angle bisector
[tex]\overline {BD}[/tex] bisects ∠ABC [tex]{}[/tex] Given
∠ABD ≅ ∠CBD [tex]{}[/tex] Definition of angle bisector
[tex]\overline {BD}[/tex] ≅ [tex]\overline {BD}[/tex] [tex]{}[/tex] Reflexive Property
ΔABD ≅ ΔCDB [tex]{}[/tex] ASA
The Angle-Side-Angle ASA, ASA, congruency postulate, states that if two angles and the included side of one triangle is congruent to two angles and the included side of another triangle, then the two angles are congruent.
A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second car has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 825 miles, for total gas cumsumption of 40 gallons. How many gallons were consumed by each car
Answer:
Number of gallons consumed by first car = 15 gallons
Number of gallons consumed by second car = 25 gallons
Step-by-step explanation:
Given that:
Fuel efficiency of first car = 30 miles per gallon
Fuel efficiency of second car = 15 miles per gallon
Total distance traveled = 825 miles
Total gas consumption = 40 gallons
To find:
Number of gallons consumed by each car = ?
Solution:
Let the number of gallons consumed by first car = [tex]x[/tex] gallons
As per question statement, number of gallons consumed by second car:
[tex]40-x[/tex]
Number of miles covered by a car = Fuel efficiency [tex]\times[/tex] Number of gallons consumed
Number of miles covered by first car = 30 [tex]\times[/tex] [tex]x[/tex]
Number of miles covered by second car = 15 [tex]\times[/tex] ([tex]40-x[/tex])
Using the given statement:
[tex]30x+15(40-x)=825\\\Rightarrow 30x+600-15x=825\\\Rightarrow 15x=225\\\Rightarrow x =15\ gallons[/tex]
Therefore, Number of gallons consumed by first car = 15 gallons
Number of gallons consumed by second car = 40 - 15 = 25 gallons
slove the product of
[tex]1345 \times {10}^{1} = ?[/tex]
then explain how you moved the demal to get the product
Answer:
1.345
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
9% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?
Answer:
9/100.
Step-by-step explanation:
9% is equal to about 9/100. 9/100 is the simplest form.
what is the answer to 3(-4x-5)
Answer:
-12x -15
Step-by-step explanation:
3(-4x-5)
3*-4x -3*5
-12x -15
Answer:
-12x-15
Step-by-step explanation:
expand and simplify
-12x-15
Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answer:
I think it’s 11 but not sure
Step-by-step explanation:
Answer:
11.4017543
(round if you're supposed to)
Step-by-step explanation:
It is a right triangle so you can use the pythagoreum theorem.
a(a) + b(b) = c(c)
a and b: legs
c: hypostenuse
9 and 7 are legs
the unknown is the hypostenuse
9(9) + 7(7) = c(c)
81 + 49 = c(c)
130 = c(c)
square root of 130 is 11.4017543
c(c) = 130
c = 11.4017543
Please help. Will award brainliest:)
help plz & thank you!!
Answer:
x=(-6)
Step-by-step explanation:
Answer:
x= -6
Step-by-step explanation:
5x-10= -40
add 10 to both sides
5x= -30
divide both sides by 5
x= -6
xoxo, your highness...In a certain chemical, the ratio of zinc to copper is 4 to 17. A jar of the chemical contains 357 grams of copper. How many grams of zinc does it contain?
Answer:84
Step-by-step explanation:
MY TEACHER IS IGNORING ME! PLEASE HELP 10 POINTS !
Mai biked 6 3/4 miles today, and Noah biked 4 1/2 miles. How many times the length of Noah’s bike ride was Mai’s bike ride?
Thanks in advance
Answer:
Tell ur teacher to stop ignoring you 23
Step-by-step explanation:
ur welcomw 32
What is the radius and diameter of the following circle?
11 cm
Answer:
Diameter is 11cm, and the radius is 5.5
Step-by-step explanation:
To get the radius, just divide the size of the circle by 2
Diameter is the same size as the circle
BRAINLIEST TO RIGHT ANSWER! ASAP!
Answer:
y=-1/2x+1
Step-by-step explanation:
Solve the following: Eric’s father works two part-time jobs, one in the morning and one in the afternoon, and works a total of 40 hours each 5-day workweek. If his schedule is the same each day, and he works 3 hours each morning, how many hoursdoes Eric’s father work each afternoon?The equation for this math problem is 5(a +3) =40 What does the 5 represent? * What is a?
Saman drives a truck for $15 an hour. If she worked 40 hours, what would be her gross earnings for one week?
Answer:
$600
Step-by-step explanation:
because 40 hours at a rate of $15/hours adds up to $600.
(40*15= 600)
what is 5/8 divided by 4
Answer:
0.156
Step-by-step explanation:
Answer:
5/32
Step-by-step explanation:
[tex] \frac{5}{8} \div 4 \\ \\ = \frac{5}{8} \times \frac{1}{4} \\ \\ = \frac{5 \times 1}{8 \times 4} \\ \\ = \frac{5}{32} [/tex]
The graph of function f is shown. Function g is represented by this equation. g(x) = 2(2)x Which statement correctly compares the two functions? A. They have different y-intercepts and different end behavior. B. They have the same y-intercept but different end behavior. C. They have different y-intercepts but the same end behavior. D. They have the same y-intercept and the same end behavior.'
The graph of the function f and graph of the function g(x) have the different y-intercept but have the same end behavior option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a graph of a function f and a function g(x) is:
[tex]\rm g(x) = (2)2^x[/tex]
If draw a graph of g(x) on the coordinate plane, it will be a exponential function.
For y intercept of g(x):
x = 0,
y = 2
But graph of a function f and graph of a function g(x) has same end behavior.
Thus, the graph of the function f and graph of the function g(x) have the different y-intercept but have the same end behavior option (C) is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
Find (x^3+7x^2-16x-112) divide (x+4) by using synthetic division.
Answer:
x^2+3x-28
Step-by-step explanation:
Answer:
The answer is x^2 3x 28
Step-by-step explanation:
Someone help me pls!!!!
Answer:
it b
Step-by-step explanation:
15 out of 20 students own hand-held games; 105 out of 160 students own hand held games. PLEASE HELP ME ASAP
Answer: No the ratios are NOT related
Step-by-step explanation:
SOMEONE PLEASE HELP ME WITH THIS!
Answer:
(−1)(5x+2)
Step-by-step explanation:
I googled it
Answer:
(x-1)(5x+2)
Step-by-step explanation:
5[tex]x^{2}[/tex] + 2x - 5x - 2
(5[tex]x^{2}[/tex] + 2x) (- 5x - 2)
x(5x + 2) -1(5x + 2)
(x-1)(5x+2)
Select the correct answer.
Which inequality will have a dashed boundary line with a shaded area above its graph?
A. 7x − y ≤ 3
B. x − y ≤ 4
C. 2x − 9y > 2
D. 4x + 7y > 3
PLEASE HELP FAST MAKE SURE YOU READ IT CORRECT I WILL GOVE BRAINLIST AND EXTRA POINTS PLEASE HELP!
Answer:
f(5) = 3
Step-by-step explanation:
f(x) is the y coordinate at x.
At x = 5, y = 3, so f(5) = 3.
Find the volume of the pyramid below.
7.2 in
9.7 in
Answer:
23.28 inches (im not sure if this is correct because you need length, height, and width.)
Step-by-step explanation:
lwh
3
1. Fiona Wolfe regular pay is $9 an hour and time-and-a-half for anything over 40 hours. Last week she worked 46 hours at her full-time job. She also worked 7 hours last week at a part-time job that pays $11 an hour. What total gross pay did she earn last week from both jobs?
Answer:
$518
Step-by-step explanation:
The total gross payment = full-time payment + part-time payment
Given that:
She worked 46 hours for her full-time payment and time-and-a-half for anything and she is being paid $9 per hour;
and also worked for 7 hours for her part-time payment and she is being paid $11 per hour and time-and-a-half for anything
Then, the total gross payment = $46(9 1/2) + $7(11 1/2)
The total gross payment = $46(9.5) + $7(11.5)
The total gross payment = $437 + $80.5
The total gross payment = $517.5
The total gross payment ≅ $518