Answer:
1.97 day; 1 day.
Step-by-step explanation:
0.07*100 = 7
31.91x - 7 = 70
70 - 7 = 63
31.91x = 63
63 / 31.91 = 1.97
Hudson can afford to drive the car for 2 days and stay under his budget.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We know that it costs $0.07 for every mile driven and we plan to drive 100 miles, that means we can set the inequality as:
31.91x + 0.07(100) ≤ 70
31.91x + 7 ≤ 70
Rearranging the inequality so we have the variable isolated on one side, we get:
31.91x ≤ 63
Divide both sides by 31.91 to get x alone.
x ≤ 1.97430
x ≤ 2
From obtaining the solution, Hudson can afford to drive the car for 2 days and stay under his budget.
Learn more about the inequalities here:
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The question seems incomplete, the complete question would be as:
A rental car company charges $31.91 per day to rent a car and $0.07 for every mile driven. Hudson wants to rent a car, knowing that:
• He plans to drive 100 miles.
• He has at most $70 to spend.
Which inequality can be used to determine, the maximum number of days Hudson can afford to rent for while staying within his budget?
John jumped 32 inches. Ella jumped 1 foot farther than John jumped. How far did Ella jumped?
2 ft 8 in
8 ft 6 in
3 ft 8 in
7 ft 2 in
50 points each question. Please help. How do I solve?
[tex]~~~~y= \sec^{-1} (14x)\\\\\\\implies \dfrac{dy}{dx} = \dfrac{1}{14x \sqrt{(14x)^2 -1}} \cdot 14\\\\\\\implies \dfrac{dy}{dx}=\dfrac{1}{x\sqrt{196x^2 -1}}\\\\\\\text{At point,}~~ (x_1,y_1) = \left(\dfrac{\sqrt2}{14}, \dfrac{\pi}4} \right), \text{slope of the tangent line,}\\\\\\m = \dfrac{dy}{dx} = \dfrac{1}{\dfrac{\sqrt 2}{14} \sqrt{196 \left(\dfrac{\sqrt 2}{14} \right)^2-1}} \\\\\\~~~~~~~~~~~=\dfrac{14}{\sqrt 2 }\\\\\\~~~~~~~~~~~=\dfrac{7\sqrt 2 \sqrt 2}{\sqrt 2}\\\\\\[/tex]
[tex]=7\sqrt 2\\\\\\\text{Equation of tangent line,}\\\\\\~~~~~y-y_1 = m(x -x_1)\\\\\\\implies y- \dfrac{\pi}4 = 7\sqrt 2 \left(x - \dfrac{\sqrt 2}{14} \right)\\ \\\\\implies y= 7x\sqrt 2 - 1+ \dfrac{\pi}4[/tex]
The profits earned in a year by some companies in a city are shown $160,000 $140,000 $130,000 $1120,000 $150,000 based on the data should the mean, or the median Be used to make the inference about the profits earned by the companies
Answer:
Median
Step-by-step explanation:
In this data set, there's a huge outlier ($1,120,000) which would skew the results upwards. Using the mean to make an inference about the profits would better represent the whole data set since you'd get $150,000 which is more in line with the rest of the data point.
Subtraction is the reverse operation of_____
Answer:
addition !
Step-by-step explanation:
Answer: subtraction is the reverse operation of Addition
Step-by-step explanation: Hope this helps,
Which ordered pair is a solution to the following system of inequalities? y ≤ –x2 + 8x y > x2 – 3 (–1, 4) (0, 9) (2, 7) (4, 3)
Answer:
(2, 7)
Step-by-step explanation:
(2, 7) are the coordinate which ordered pair is a solution to the following system of inequalities [tex]y \leq -x^2 + 8x \\[/tex] and [tex]y > x^2 - 3[/tex].
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
we want to find which ordered pair is a solution to the following system of inequalities.
[tex]y \leq -x^2 + 8x \\[/tex]
[tex]y > x^2 - 3[/tex]
The solution of a inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the inequality is the graph of all solutions of the system.
Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality.
[tex]y \leq -x^2 + 8x \\\\y = -x^2 + 8x\\\\y > x^2 - 3\\\\[/tex]
x = 2 and y = 7
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A ball has a mass of 3g and a volume of 6 cm3. It's density is what
and will it float or sink
in water.
Answer:
float
Step-by-step explanation:
density = mass/voume
3g/6c.m. ^3
0.5g/c.m.^3 = 0.5g/mL^3
Since the density of water is about 1g/mL^3 and 0.5g/mL^3 is less than that, it will float
pls view the calculations section of this ans for more details.
Calculations ↓[tex]\boxed{\\\begin{minipage}{3cm}\xrightarrow{density}\\$\displaystyle\frac{mass}{volume} \\ \end{minipage}}[/tex]
Mass = 3g
Volume = 6
3/6
1/2 <----- density
So the density is 1/2 mL³It will float because it's density is less than the density of waterhope helpful ~
13-28 Sketch the region enclosed by the given curves and find its area.
24. [tex]y=\cos x, \quad y=1-\cos x, \quad 0 \leqslant x \leqslant \pi[/tex]
Answer:
rea (A) 0.0682
Step-by-step explanation:
The sketch for the region enclosed by the given curves can be found in the image attached below.
From the image below;
The two curves intersect in the area of tan 9x = 2 sin 9x
Recall that:
making x the subject; then:
The subdivision of the domain is in two intervals
where;
Area (A) =
Area (A) = 0.06818
Area (A) 0.0682
Solve the equation 9(k-2)=- 6. ( slove for k
Answer:
k=4/3
Step-by-step explanation:
9(k-2)=-6
-expand the bracket
9k-18=-6
-keep "k" on one side
9k=12
-divide both sides by 9 to get k
k=4/3
Solve the equation by using the quadratic formula.
8x2 – 2x - 15 =0
Answer:
x = 3/2 or x = -5/4
Step-by-step explanation:
Solve for x over the real numbers:
8 x^2 - 2 x - 15 = 0
Using the quadratic formula, solve for x.
x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:
x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16
Simplify radicals.
sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:
x = (2 + 22)/16 or x = (2 - 22)/16
Evaluate (2 + 22)/16.
(2 + 22)/16 = 24/16 = 3/2:
x = 3/2 or x = (2 - 22)/16
Evaluate (2 - 22)/16.
(2 - 22)/16 = -20/16 = -5/4:
Answer: x = 3/2 or x = -5/4
Fill in the blank with the correct number to balance the equation: 4Cr + 3O2 → Cr2O3
Answer:
2
Step-by-step explanation:
Explanation and answer please
Answer:
$41.96
Step-by-step explanation:
30% of 59.95 is 17.99 (rounding to the nearest hundredth place since it was 17.985)
subtract 17.99 since it is the sale (30%)
59.95 - 17.99 = 41.96
the cd is worth $41.96 on sale for 30% off.
Find - 3a - 6 when a = - 2. Write the answer in simplest form.
Answer:
-3(-2) - 6
6 - 6
= 0
Answer:
0
Step-by-step explanation:
-3a-6=-3×-2-6=6-6=0
A circle has a radius of 11.4 cm
What is the exact length of an arc formed by a central angle measuring 120°?
Enter your answer in the box. Express your answer using .
NEED HELP QUICK!!!
Answer:
7.6pie
Step-by-step explanation:
120°/360°=X/11.4×2 pie
1/3×22.8 pie =X
X= 7.6 pie
Please help on math.
Answer:
[tex]\fbox{625 \: dollars }[/tex]
Step-by-step explanation:
Given:
from circular graph,
Savings by Oliver's = 25% of Total budget
Monthly budget = $ 2500
To find:
How much money does Oliver save?
Solution:
From diagram we came to know that,
Oliver's saving is 25% of total monthly budget.
Hence the money he saves each month will be 25% of $2500(Monthly budget)
To calculate the X percent of any given real number multiply the number with X and divide it by 100.
[tex] \sf \hookrightarrow \: 25 \% \: of \: 2500 \\ \sf \hookrightarrow 2500 \times \frac{25}{100} \\ \sf \hookrightarrow 2500 \times \cancel\frac{25}{100}_4 \\ \sf \hookrightarrow \: \frac{2500}{4} \\ \sf \hookrightarrow \cancel{\frac{2500}{4}} \: ^{625} \\ \sf \hookrightarrow \fbox{625 \: dollars }[/tex]
625$ does Oliver saves each month.
Thanks for joining brainly community!
The transformation (x, y) to (x+4, y-3) is preformed on the line segment AB. The image is the line segment A'B' where point A' = (3, -3) and point B' = (5, -3). What are the coordinates of A and B in line segment AB?
A) A = (-1, 6), B = (1, -6)
B) A = (-1, 0), B = (1, 0)
C) A = (7, 6), B = (9, -6)
D) A = (7, 0), B = (9, 0)
Answer:
B) A = (-1, 0), B = (1, 0)
Step-by-step explanation:
If the transformation of AB to A'B' is (x+4, y-3),
then the transformation of A'B to AB is the reverse: (x-4, y+3)
Given
A' = (3, -3) → A = (3-4, -3+3) = (-1, 0)
B' = (5, -3) → B = (5-4, -3+3) = (1, 0)
Therefore:
A = (-1, 0), B = (1, 0)
f(x)= 4/5x +7
What is the value of f(5)?
Answer: 11
Step-by-step explanation:
Please help me I need help asap
Answer:
AB = 23 , BC = 13
Step-by-step explanation:
Isosceles mean two side angle is equal to each other.
AB and AC are the same. So we can solve for x.
[tex]AB=AC\\5x-7=23\\5x=30\\x=6\\\\AB = 5x-7\\AB = 5*6-7\\AB=30-7\\AB = 23\\\\BC = 3x-5\\BC = 3*6-5 = 18 - 5 = 13\\BC = 13[/tex]
Answer:
Step-by-step explanation:
Because they tell us it's an isosceles triangle we know two sides are the same length. since AB and AC look like they are similar we can assume that those sides are the exact same length. Since we know , now, that AB and AC are equal in length, set them equal
AB = AC
now plug in given info
5x-7 = 23
nice, now use your super hero algebra skillz to solve for X. My calculus prof. always says that students are bad at algebra, i'll help you do the algebra.
5x-7=23 ( add 7 to both sides)
5x=23+7 (add 7 to 23 )
5x=30 (divide both sides by 5 )
x=6
yay, we have X now.
we know AB =23 , because of the isosceles triangle thing.
BC = 3x-5
plug in for X :)
3*6-5=BC
18-5=BC
13=BC
Yay, all the answers, and way to get the answers are above :P
complete the table of values for y=x^2-4x+3
x=1
y=1²-4(1)+3=1-4+3=0x=2
y=2²-4(2)+3=4-8+3=7-8=-1x=3
y=3²-4(3)+3=9-12+3=12-12=0For each value of w, determine whether it is a solution to -8+5w >32.
Answer:
• no
• no
• no
• yes
Step-by-step explanation:
Let's start by solving the inequality.
-8 +5w >32
5w> 32 +8
5w> 40
Divide both sides by 5:
w> 8
This means that the value of w should be greater than 8.
Since w is not ≥8, the value of w does not include 8. -6 and -5 are smaller than 8 and are thus not the value of w either.
9, being greater than 8, is a solution to the inequality.
Is x = 0 a valid potential solution to the equation log(x + 2) + log(x + 5) = 1? (You don't need to solve this equation, just determine if x = 0 is a valid solution) Question 22 options: No, because log(0) is undefined. No, because the logarithm of a negative value is undefined. It can't be determined from the information given. Yes, since log(2) and log(5) both exist as valid values for the logarithm.
Answer:
Yes, since log(2) and log(5) both exist as valid values for the logarithm.
didnt check if ur equation is correct though
What is value of 5 in 2 500.7
Answer:
500
Step-by-step explanation:
Since the 5 is in the hundreds place in the number 2500.7, its value is 5 * 100 = 500.
Answer:
hundreds
Step-by-step explanation:
Which expression is equivalent to 4x+2y-8x
a) 2(3y-2x)
b) 2 (4y-2x)
c) 2(2y+3x)
d) 2(3x-2y)
Simplify 2x-- yfor x = 3 and y=-2.
•20
•14
•16
•10
Answer:
8 (none of the above)
Step-by-step explanation:
Given that,
→ x = 3
→ y = -2
Let's solve the equation,
→ 2x - y
→ 2(3) -(-2)
→ 6 + 2
→ 8 is the answer.
50 POINTSSS AND WILL GIVE BRAIN
Look at the graph attached
What is the domain?
–6 ≤ x ≤ 4
–6 ≤ x ≤ 4, x ≠ –6, 2
–12 ≤ x ≤ 10
–12 ≤ x ≤ 10, x ≠ –6, 6
Domain: All possible x-values
Starting at the left side, the smallest value of the domain is -12. There is a break at x = -6, but there is still a closed circle, which means that there IS a value for -6. The same occurs at x = 6. The largest x-value of this graph is 10.
Therefore, the domain is -12 <= x <= 10
Hope this helps!
One positive integer is 1 less than twice another. The sum of their squares is 461. Find the integers.
Answer:
10 and 19
Step-by-step explanation:
In Algebra, an even number = 2x, because anything multiplied by 2 is even.There are two numbers in the question, I'll define the first one as 2xthe other number is 1 less than twice of the first, so I'm going to define it in algebra as 2(2x) - 1, which is just 4x - 1the square of the first is [tex]4x^2[/tex]the square of the second is [tex]16x^2-8x+1[/tex]add them together: [tex]20x^2-8x+1[/tex]this equation = 461, so [tex]20x^2-8x+1 = 461[/tex]simplify to [tex]20x^2-8x-460 = 0[/tex]I wont explain how to solve this here, since it is very complicated, if you don't know search up solving quadratics.the solutions are 5 or -4.6, it cannot be -4.6 since the question says positive, so the solution for x = 5substitute x into our equations for the two numbers in steps 1 and 2the first number = 10, the second = 19Juana and Andy completed 10 math problems total. Juana completed 6 of the problems. Write an equation to determine the number of math problems that Andy completed, then solve the equation. How many of the math problems did Andy complete?
Step-by-step explanation:
let the number of questions solved by Andy=x
this implies that 6+x=10
making x the subject of the equation
x=10-6
x=4
therefore Andy solved 4 questions
chase deposits $7440.93 into a savings account that pays a simple annual interest rate of 1.23%
Answer:
To find how much money Chase will get in a certain amount of years, set up the following equation:
(7440.93*0.0123)*x = y
Plug in x. "x" stands for how many years Chase keeps the money in his account while earning interest.
Keep "y" unknown, as that stands for what you are trying to solve for, which is how much interest money Chase will make.
Find the smallest whole number by which 2268 should be multiplied so as to
get a perfect square number. Also find the square root of the square number
so obtained.
Answer:
Correct option is B)
252=
2×2
×
3×3
×7
The prime factor 7 does not appear in pairs. To make 252 a perfect square we need one more 7.
Hence, the smallest number by which 252 must be multiplied so that
the product is a perfect square is 7.
And, 252×7=
2×2
×
3×3
×
7×7
252×7
=
2×2
×
3×3
×
7×7
=2×3×7=42
Step-by-step explanation:
To find the smallest whole number by which 2268 should be multiplied to get a perfect square, we need to factorize 2268 into its prime factors. Then, we can determine which prime factors are needed to make the number a perfect square.
The prime factorization of 2268 is:
2268 = 2^2 * 3^2 * 7 * 9
To make it a perfect square, we need to include the missing factors. In this case, we are missing a factor of 2 and a factor of 3. Therefore, we need to multiply 2268 by 2 * 3 = 6.
2268 * 6 = 13608
Now, we have a perfect square number, 13608.
To find the square root of 13608, we can take the square root of each of its prime factors:
√(2^2 * 3^2 * 7 * 9)
= √2^2 * √3^2 * √7 * √9
= 2 * 3 * √7 * 3
= 6 * √7
So, the square root of the square number 13608 is 6√7.
x/9 times 15-47=28
help pls
Answer:
x=45
Step-by-step explanation:
Then,
x/5(15)-47=28
Step 1: Simplify the equation on both sides
x/9(15)-47=28
5/3x-47=28
Step 2: Add 47 to both sides
5/3x-47+47=28+47
5/3x=75
Step 3: Multiply both sides by 3/5
(3/5)*(5/3x)=(3/5)*(75)
x=45
43. Find an equation of the tangent line to the curve [tex]y=10^{x}[/tex] at the point (1,10)
Answer:
23x-y=13
Step-by-step explanation:
we need to find the derivative with respect to x
In(y) =In(10^x)
In(y)=xIn(10)
now we have to take the derivative with respect to x
Therefore, y'=yIn(10)
where y'=10^xIn(10), Chain rule!
note: First derivative function always give us the gradient value when x value is substituted in
Therefore, at x=1, our gradient will be m= 10^1In(10)
Gradient m=23.0 to the nearest tenth
Finding the equation of the line
y-y1=m(x-x1)
y-10=23(x-1)
y-10=23x-23
y-23x=-23+10
y - 23x = -13
so, the equation of the line tangent line is
23x - y =13