Missing Parts
Here are the formulae to work out the thinking distance and the braking distance for a car traveling at V miles per hour.
Thinking distance = V feet
[tex]\text{Braking distance = }\dfrac{V^2}{20}$ feet[/tex]
(a) A car is traveling at 70 miles per hour. What is the total stopping distance for this car? feet
(b) A different car is traveling so that its braking distance is 125 feet. How fast is the car traveling? miles per hour
Answer:
(a)2520 feet
(b)50mph
Step-by-step explanation:
Total Stopping Distance = Thinking Distance + Braking Distance
Given that for a car traveling at V miles per hour:
Thinking distance = V feet
[tex]\text{Braking distance = }\dfrac{V^2}{20}$ feet[/tex]
We have:
[tex]\text{Total Stopping Distance=} (V+\dfrac{V^2}{20})$ feet[/tex]
(a)V=70 miles per hour
[tex]\text{Total Stopping Distance=} 70+\dfrac{70^2}{20}$=2520 feet[/tex]
The total stopping distance for a car traveling at 70 miles per hour is 2520 feet.
(b)
Braking Distance = 125 feet
[tex]\text{Braking distance = }\dfrac{V^2}{20}$ feet[/tex]
Therefore:
[tex]\dfrac{V^2}{20}=125\\\\V^2=125\times 20\\V^2=2500\\V^2=50^2\\V=50$ miles per hour[/tex]
A car with a braking distance of 125 feet is traveling at a speed of 50mph.
Name the point of intersection.
Answer:
F
Step-by-step explanation:
Answer:
The point of intersection is F as that is the point where both lines cross each other, and since that is the only point where both lines go through it, it is the point of intersection.
Simplify the variable expression by evaluating its numerical part, and enter your answer below. g - 2/2
Answer:
g - 1
Step-by-step explanation:
g - 2/2
2/2 = 1
g - 1
48:PLEASE HELP Find the x-intercept of -x+2y=22
Answer:
-22
Step-by-step explanation:
set y equal to zero and solve like a regular singular variable equation
Which are the roots of the quadratic function f(b) = b2 - 75? Select two options
Answer: Option A, & B
(A) b = 5 StartRoot 3 EndRoot b= 5[tex]\sqrt{} 3[/tex]
(B) b = Negative 5 StartRoot 5 Endroot b= -5[tex]\sqrt{} 3[/tex]
Step-by-step explanation:
Suppose the linear regression line y = 3.27x + 1.52 predicts the weight of a large dog, in pounds, x weeks after it is born. About how much would the dog weigh after 6 weeks?
Answer:
y=21.14
Step-by-step explanation:
x=6 because after 6 weeks
y= 3.27(6)+ 1.52
y=19.62 + 1.52
y=21.14
8. 7 L of an acid solution was mixed with 3 L of a 15% acid solution to make a 29% acid solution. Find / 3 the percent concentration of the Ent solution. (Must use algebra!)
7 L of one solution is mixed with 3 L of another, making a new solution with a total volume of 10 L and concentration 29%. This means the new solution contains
(10 L) * 29% = (10 L) * 0.29 = 2.9 L
of acid.
Let the concentration of the first solution be c%. Each liter of the 15% acid solution contributes 0.15 L, and each liter of the solution of unknown concentration contributes 0.01c L of acid. To end up with a total of 2.9 L of acid, we would get
7 * (0.01c L) + 3 * (0.15 L) = 2.9 L
Solve for c (we can omit the units):
0.07c + 0.45 = 2.9
0.07c = 2.45
c = 35
So the first solution has a concentration of 35%.
Distribute and simplify the following: x(3x + 2)(-2x + 1)
Given the functions f (x) = x^2 + 4 and g (x) = 3x+ 8 what is a solution for the equation ? x^2 + 4 = 3x + 8 A. 0 B. 1 C. 2 D. 4
Answer:
D
Step-by-step explanation:
Let's solve your equation step-by-step.
x2+4=3x+8
Step 1: Subtract 3x+8 from both sides.
x2+4−(3x+8)=3x+8−(3x+8)
x2−3x−4=0
Step 2: Factor left side of equation.
(x+1)(x−4)=0
Step 3: Set factors equal to 0.
x+1=0 or x−4=0
x=−1 or x=4
Answer:
x=−1 or x=4
Solve the inequality -12 ≤ 2x -4 < 10
Answer:
-4 ≤ x <7
x is greater than or equal to -4, and x is less than 7
Step-by-step explanation:
Take each side and solve
-12 ≤ 2x -4
subtract 4 on both sides
-8 ≤ 2x
divide by 2 on both sides
-4 ≤ x
2x -4 < 10
add 4 on both sides
2x < 14
divide by two on both sides
x < 7
Final answer:
-4 ≤ x <7
Answer:
-4 ≤ x < 7
Step-by-step explanation:
Method 1: Split the inequality into two parts,
-12 ≤ 2x-4
and
2x -4 < 10
Solve.
-8 ≤ 2x
2x ≥ -8
x ≥ -4
and
2x < 14
x < 7
So, x is greater than (or equal to) -4, but less than 7.
-4 ≤ x < 7
Method 2:
-12 ≤ 2x - 4 < 10
Add 4 to both sides.
-8 ≤ 2x < 14
Divide both sides by 2.
-4 ≤ x < 7
Help!!!!! please!!!!!
Hey there! :)
Answer:
Choice D. V = 2184 in³.
Step-by-step explanation:
Recall that to find the volume of a rectangular prism, the following formula is used:
V = l × w × h
Plug in the given dimensions into the formula to solve for the volume:
V = 14 × 13 × 12
Multiply:
V = 2184 in³. The correct answer is D.
Answer:
2,184 inches^3
Step-by-step explanation:
Well to find the volume of a rectangular prism we have to use the following formula l*w*h.
The l is length which is 14 the w which is width which is 13, and the h which is height which is 12.
So we do 14*12*13 which is 2,184 inches^3.
PLEASE HELP, I WILL MARK YOU BRAINIEST Identify if the relationship represented in the tables below is linear. If the table is linear, write the equation of the line.
Answer:
a) Yes. y=-4x+2. b) No.
Step-by-step explanation:
a) For every section of the graph as x goes up 1, y does down 4. It has a proportional relationship and you can use the rise and run found to do rise/run and get a slope of -4 and when x is at 0, y is at 2, giving you a y-intercept of 2.
b) There is no proportional relationship using addition and subtraction so the graphed line would not be straight.
using y2-y1 over x2-x1 the first table is 10-14 over -2--3 which would be -4 over 1
The next one would be 4 over -1
Not 100 percent sure
Can someone help me please
Answer: y = 6
Step-by-step explanation:
A square's area can be done by using s^2, where s is y in this case. Because there are 5 squares, the area of the figure is 5y^2. Because the area is also 180cm, 5y^2=180.
Then divide both sides of the equation by 5 to get y^2 = 36. Then square root both sides of the equation to get y = 6.
Hope it helps <3
PLEASE HELP ME IM BEGGING
❗️10 points❗️
24. Find slope of the line.
A. 3/2
B. -3/2
C. -2/3
D. 2/3
Answer:
A
Step-by-step explanation:
the equation go from a negative Y value, to positive. The answer is A because it goes from (-2,-2), towards (0,1) increasing the Y value by 3, and the X by 2
Find the area of triangle ABC. Give your answer correct to 1 decimal place.
Answer:
83.3 cm²
Step-by-step explanation:
First we should calculate the height of this triangle using the pythagorian theorem
Let h be the height of the triangle :
7²+12²= h² h = [tex]\sqrt{12^{2}+7^{2} }[/tex]= [tex]\sqrt{193}[/tex]Let A be the area of the triangle :
A= (b*h)/2=(12*[tex]\sqrt{193}[/tex])/2=83.3 cm²Answer:
31.7 cm^2
Step-by-step explanation:
We can use the formula
A = 1/2 ab sin C where a and b are two sides and C is the angle between them
C = 180 - 72 - 59 = 49
A = 1/2 ab sin C
= 1/2 ( 7)(12) sin 49
31.69780237
To 1 decimal place
31.7 cm^2
It says to calculate the area of the sector and t round to the nearest hundredth and to use 3.14 for Pi
Answer:
Step-by-step explanation:
The formula for the area of a sector is
[tex]A=\frac{\theta}{360}*\pi r^2[/tex] where theta is the measure of the central angle (which is the same measure as that of the arc that is intercepted by the 2 radii formig the angle), and r is the radius.
For us, theta is 90 degrees and r is 20. Filling in the formula:
[tex]A=\frac{90}{360}*(3.14)(20)^2[/tex] which simplifies down a bit to
[tex]A=\frac{1256}{4}[/tex] so
A = 314 m squared
Enter the correct number word to complete the conversion. 1 milliampere = one ? of an ampere
Answer:
One milliampere is equal to 0.001 ampere.
Step-by-step explanation:
Mili, refers to thousandth. (for example, millimeter or milliliter.)
one and two third minus tow and one third?
Answer:
-2/3
Step-by-step explanation:
Step 1: Write out expression
1 2/3 - 2 1/3
Step 2: Convert to improper fractions
5/3 - 7/3
Step 3: Subtract
-2/3
Answer:
[tex]\frac{-2}{3}[/tex]
Step-by-step explanation:
[tex]1 \frac{2}{3} - 2\frac{1}{3} \\\\[/tex]
[tex]\frac{5}{3} - \frac{7}{3} = \frac{-2}{3}[/tex]
Hope this helps! :)
The principal represents an amount of money deposited in a savings account subject to compound interest of a given rate.How much money there will be in the account after the given number of years. The principal is$5000, 5% Rate, quarterlybover a two year period.
Answer:
$5522.43
Step-by-step explanation:
The amount in an account for a principal P saved at compound interest for a duration of n years compounded with period k at an annual interest rate of r% is calculated using the formula:
[tex]A(n)=P(1+\frac{r}{k})^{nk}[/tex]
In this case:
Principal, P=$5000Interest Rate, r=5%=0.05Time, n=2 yearsPeriod, k=4(Quarterly)Therefore, the amount is:
[tex]A(n)=5000(1+\frac{0.05}{4})^{4*2}\\=5000(1+0.0125)^{8}\\=5000(1.0125)^{8}\\=\$5522.43[/tex]
The amount of money in the account at the end of the two years is $5522.43.
which of these shapes are parallelograms choose all correct answers
Answer:
The 2 pink ones
explanation: I got this right
The two pink diagrams in the given figure are parallelograms.
What is a parallelogram?A unique kind of parallelogram created with parallel lines is called a parallelogram.
A parallelogram can have whatever angle between its neighboring sides, but for it to be a parallelogram, it's opposite sides must be parallel. If a quadrilateral's opposite sides are parallel and congruent, it will be a parallelogram.
So a rectangle both with pairs of separate sides being parallel and equal is known as a parallelogram.
The word "parallelogram" is a translation of the Greek term "parallelogrammon," which means "confined by line segments." As a result, a quadrilateral that is surrounded by parallel lines is called a parallelogram.
To know more about Parallelogram:
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2x - y = 6
2x - 2y = 4
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▹ Answer
(4, 2)
▹ Step-by-Step Explanation
2x - y = 6
2x - 2y = 4
2x = 6 + y
2x - 2y = 4
6 + y - 2y = 4
y = 2
2x - 2 * 2 = 4
x = 4
(x, y) = (4, 2)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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Answer:
x = 4 and y = 2Step-by-step explanation:
Using elimination method
2x - y = 6........ 1
2x - 2y = 4 ......... 2
Subtract equation 2 from 1
That's
2x - 2x - y + 2y = 6 - 4
y = 2
Substitute y = 2 into any of the equations
Using equation 1
2x - 2 = 6
2x = 6+2
2x = 8
Divide both sides by 2
x = 4
Therefore x = 4 , y = 2
Hope this helps you
Please answer it now in two minutes
Answer:
p = 67
Step-by-step explanation:
The polygon has 8 sides.
The sum of the measures of the interior angles is:
180(n - 2) = 180(8 - 2) = 180(6) = 1080
p + 49 + 2p + 7 + 2p + 142 + p + 50 + 2p + 147 + 2p + 15 = 1080
10p + 410 = 1080
10p = 670
p = 67
Find the value of y for the given value of x. Round to the nearest hundredth. y = 15 + 3 ln x; x = 7.2
Answer:
y = 20.922
Step-by-step explanation:
Simply plug in x and evaluate:
y = 15 + 3ln(7.2)
Only way to calculate ln is to plug into a calc:
We should get 20.9222 as our answer.
.Calculate the time in which ₦1,500 will amount to ₦9,000 at 20% per annum.
Answer:
30 yrs
Step-by-step explanation:
SI = PRT/100
T = I × 100/PR
= 9000×100/1500×20
= 900000/30000
= 30 yrs
HELP ME PLEASE PLEASE
Answer:
The solution to the system is (-6, -9)
Step-by-step explanation:
In order to graph the system, we can find two points belonging to each equation and join them with a line. We look then for the point at which the lines intersect.
(a) Two points for the first line defined by: 3 x + 2 y = -36
What is the value of y when x=0?
3 (0) + 2 y = -36
then y = -36/2 = -18, then one point on this line is (0, -18)
What is the value of x when y = 0?
3 x + 2 (0) = -36
then x = -12, then a second point for this line is: (-12, 0)
When can draw the line that represents this first equation by joining the two points as shown in the attached image with the two points found and the line depicted in orange.
(b) Two points for the second line defined by: - x + 2 y = -12
What is the value for y when x = 0?
- (0) + 2 y = -12
then y = -12/2 = -6, therefore one point for this line is: (0, -6)
What is the value of x when y = 0?
- x + 2 (0) = -12,
then x= 12,and therefore another point for this line is (12. 0)
When can draw the line that represents this second equation by joining the two points we found, as shown in the attached image with the two points found and the line depicted in blue.
We see that the intersection of the two lnes takes place at x= -6 and y = -9. That is at the point (-6, -9)
What expression has the same meaning as 3 5/4?
Answer:
[tex]\sqrt[4]{3^{5} }[/tex]
Step-by-step explanation:
Using the rule of radicals/ exponents
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]3^{\frac{5}{4} }[/tex]
= [tex]\sqrt[4]{3^{5} }[/tex]
help asap please and thank you!!
Answer:
[tex] \angle T \cong \angle Z[/tex]
Step-by-step explanation:
[tex]\because \triangle QPT \cong \triangle ARZ... (given) \\
{ \purple{ \bold{\therefore \angle T \cong \angle Z.. (c.a.c.t.)}}}[/tex]
Which one of the following gives the gradient of the line shown above?
A: 3/2
B: -2/3
C: 2/3
D: 6
E: -3/2
Answer: A: 3/2
Step-by-step explanation:
When we have a line that passes through the points (x1, y1) and (x2, y2), the slope of this line is:
s = (y2 - y1)/(x2 - x1)
In this graph we can see that the line passes through the points:
(0, - 3) and (2, 0)
Then the slope is:
s = (0 - (-3))/(2 -0) = 3/2
Then the correct option is A.
The gradient of the line shown above is A: [tex]\frac{3}{2}[/tex]
Slope of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is :
slope [tex]=\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]
Now, from the given graph we can see that the line passes through the points:
(0, - 3) and (2, 0)
The slope is:
[tex]s = \frac{(0 - (-3))}{(2 -0)} \\=\frac{3}{2}[/tex]
Therefore the correct option is A.
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Zack bought 5 blue ties and 4 red ties. He will choose one at random to wear tomorrow. Find the probability that Zack will choose a red tie. Convert the fraction to a decimal. Round to three decimal places.
Answer:
0.444
Step-by-step explanation:
The total number of ties is 9, and there are 4 red ones.
So, the probability of choosing a red tie is 4/9.
4/9 = 0.444 as a decimal
What is the solution of 3+ x-2/x-3 less than or equal to 0
Answer:
The solution set consists of all the real numbers smaller than or equal to 11/4:
[tex]x\leq \frac{11}{4}[/tex]
Step-by-step explanation:
We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:
[tex]3+\frac{x-2}{x-3} \leq 0\\\frac{x-2}{x-3} \leq -3\\x-2\leq -3\,(x-3)\\x-2\leq -3x+9\\x+3x\leq 9+2\\4x\leq 11\\x\leq \frac{11}{4}[/tex]