Answer:
[tex]\boxed{22}.[/tex]
Step-by-step explanation:
Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.
If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.
Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.
To the nearest square centimeter, what is the area of the shaded sector in he circle shown below? Radius= 12 cm, angel = 110 degrees
Answer:
138.23 cm²
Step-by-step explanation:
The formula for the area of a sector is given as:
θ/360 × πr²
θ = 110°
Radius = r = 12 cm
Hence
Area of a sector = 110/360 × π × 12²
= 138.23007676 cm²
Approximately, Area of a sector = 138.23 cm²
Write the equation of the given function in vertex- and standard form.
f(x)
-2
2+
N
X
-1
0
1
2
3
4
f(x)
-5
0
3
4
3
0
The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4
What is a function?
A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
Given table is
x f(x)
-1 -5
0 0
1 3
2 4
3 3
4 0
Find the difference to find the degree of the given function
f(x) -5 0 3 4 3 0
1st difference 5 3 1 -1 -3
2nd difference -2 -2 -2 -2
The degree of the function is 2.
The general form of a second-degree function is
f(x) = ax²+bx+c
Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:
f(0) = a×0²+b×0+c
0 = c
Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:
f(1) = a×1²+b×1+0 [since c=0]
3 = a + b ....(i)
Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:
f(2) = a×2²+b×2+0 [since c=0]
4 = 4a + 2b ....(ii)
Solve equations (i) and (ii) by using the elimination method:
Multiply equation (i) by 2 and subtract it from (ii)
4a + 2b = 4
2a + 2b = 6
(-) (-) (-)
__________
2a = -2
a = -1
Putting a = -1 in equation (i):
-1 + b = 3
b = 3+1
b = 4
The function is f(x) = -x² +4x
Rewrite the given function in vertex form:
f(x) = -(x² - 4x +4-4)
f(x) = -(x-2)² + 4
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Winston has a savings in a bank and was surprised that his money
accumulated to P 65. 000 after 3 years. He knew that the bank offered him 5%
interest rate compounded bimonthly. How much was his sayings at the start?
The initial saving of the Winston was $55952.48
Compound InterestCompound interest is when you receive interest on both your interest income and your savings.
According to the question given,
Let the initial savings amount be P
We know Compound interest =
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per year
t = number of time periods elapsed
Given,
A = $65000
t = 3 years
r = 5% = 0.05
n = 2 *12 = 24
So
65000 = P(1 + (0.05/24))^72
P = $55952.48
Therefore the initial savings was $55952.48
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Please help me with this question:
What is 2x-2?
Answer:
as a factor 2(x-1) this should help or be the correcr answer
Please Answer ASAP!
Will give 85 points for answer!
Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is 13 over 17, what does the ratio 13 over 17 represent?
Answer:
Step-by-step explanation:
Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
What is a Ratio?
This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.
Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
Answer:
Step-by-step explanation:
the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning
As the number of sides of a regular polygon increases, the measure of the central angle _______.
A) increases
B) decreases
Yolanda's Flower Shop sells long-stem roses for $5 each. In addition, the
shop charges a $15 shipping fee. How many roses can Santo purchase if he
plans to spend $90?
Answer:
15
Step-by-step explanation:
5x + 15 <= 90
5x<=75
x=15
Answer:
15 roses
Step-by-step explanation:
90 (Amount Santo wants to spend)
15 (Shipping fee)
You first subtract Shipping Fee from the total amount Santo wants to spend
90-15=75
Next it's time to figure out how many roses he can buy with the $75
Each roses is $5, so you divide the left over money after shipping by the price of the rose.
75÷5=15
Solve the inequality x-4 < - 3.Then graph the solution set.show your work.
Answer:
x < 1
Step-by-step explanation:
x - 4 < - 3
+ 4 +4 Do inverse operations by adding 4 on both sides
x < 1
Therefore, the answer is x < 1.
(It isn't allowing me to attach a photo but I am just going to try make a visual of the graph below)
<------------------------------o------------------>
-4 -3 -2 -1 0 1 2 3 4
The circle is open because based on the concept that in inequalities, less/greater than and/or equal to (such as these ≥ ≤ ) signs are graphed with closed circles, while less/greater than (like these > <) signs are graphed with open circles. The direction of the arrow is moving to the left on the number line because all possible values for x would be less than 1. When graphing the inequality you would use a solid line rather than a dashed line (I had to improvise since I could not attach an image).
???????????????????????????
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (- 1, 8) ← 2 ordered pairs from the table
m = [tex]\frac{8-6}{-1-1}[/tex] = [tex]\frac{2}{-2}[/tex] = - 1 , then
y = - x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation
Using (1, 6 ) , then
6 = - 1 + c ⇒ c = 6 + 1 = 7
y = - x + 7 → B
Please help! Due tomorrow!!!
Homework assignments are worth 12 points and tests are worth 100 points. A teacher records the homework averages and test averages for 10 students. Use a graphing calculator to find an equation of the line of best fit. Round each value in your equation to the nearest tenth.
Answer:
y=7.5x+6.2
Step-by-step explanation:
Hopefully this is the answer
Answer:
y=7.5x+6.2
Step-by-step explanation:
Hopefully this is the answer
cans someone please help me
Answer:
8 x 16 = 128 (area of rectangle)
Area of triangle:
16 - 12 = 4
6 x 4 = 24
24 divided by 2 = 12 (area of triangle)
Now lets add both areas:
128 + 12 = 140 ft2 is your answer.
Seven netball teams played in a school's competition. Each team had 7 players. If 3/7 of the number of players were disqualified for poor conduct, how many pupils were qualified?
please answer correctly
A scientist studies the population of an insect colony. She begins her study with 10,000 insects in the colony and measures the population of the colony
each year. She uses the given formula to model the insect population, P, é years since the beginning of the study.
P= 10,000(1.08)
By what percent does the Insect population grow each year?
%
Solve the equation using the quadratic formula. X^2-9x+3=0
Answer:
The answer is x= [tex]\frac{9+\sqrt{69}}{2}[/tex], x= [tex]\frac{9-\sqrt{69}}{2}[/tex]
Step-by-step explanation:
x^2=a
-9x=b
3=c
Plug into formula.
Equation: [tex]\frac{9+-\sqrt{(-9)^2-4(1)(3)}}{2}[/tex]
Simplify the equation.
Equation: [tex]\frac{9+-\sqrt{81-12}}{2}[/tex]
Subtract 81 and 12.
Equation: [tex]\frac{9+-\sqrt{69}}{2}[/tex]
Spit into two equations
Equation 1: [tex]\frac{9+\sqrt{69}}{2}[/tex]
Equation 2: [tex]\frac{9-\sqrt{69}}{2}[/tex]
Hope this helps!
y = -11x - 25 ...........(i)
y = 5x - 7 ...............(ii)
Answer:
3/2
Step-by-step explanation:
5x-7=-11x-25
5x+11x=-25+7
16x=18
x=18/16
x=3/2
Type ONLY your numeric answer. You do not need the degree symbol.
Answer: 54
Step-by-step explanation:
1) First, we need to find what 'x' is. We know that the exterior angles of a triangle equal to 360. So, we will add up all the expressions and set them equal to 360.
7x-2 + 9x-31 + 4x +33 = 360.
2) We will add all the like terms, which will give us: 20x + 0 = 360. We don't need to add the 0.
3) Now, we will isolate the 'x' by dividing 360 by 20 and we will get: x= 18.
4) To find the measure of angle DCE, we just have to substitute x in '7x-2' with 18, which then would equal to: 124.
5) Now, that we have the adjacent angle of DCE, we just have to subtract 124 from 180, and we will get the answer.
6) Angle DCE equals to 54.
Consider the directed line segment from M(−3, 1) to N(3, 4). Determine which of the following statements are true.
A
The point P(1, 3) partitions the segment in the ratio 2 to 1.
B
The point Q(−1, 2) partitions the segment in the ratio 1 to 2.
C
The point R(0, 2.5) partitions the segment in the ratio 1 to 2.
D
The point S(0, 2.5) partitions the segment in the ratio 1 to 1.
E
The point T(−1, 4.5) partitions the segment in the ratio 1 to 1.
You invest $300 at 4% interest, compounded every year. What will your balance be after 5 years? (Remember, the formula is A = P(1 + r)t. ) A. $365. 00 B. $350. 96 C. $364. 65 D. $382. 88
Therefore , the solution of the given problem of interest rate comes out to be the amount after 5 years is A ≈ 364.996.
Define interest rate.With the help of an interest rate, you can determine how much borrowing will cost you and how much saving will yield. As a result, the interest rate is the cost of borrowing money and, if you're a borrower, it's expressed as a percentage of the total loan amount. An amount, expressed as a percentage of the loan amount, that a borrower is required to pay to a lender as interest during the term of a loan.
Here,
Given : Principal amount : $300
rate of interest : 4%
and time =5 years
Thus , to find the amount after 5 years as compounded
We use , the formula:
=> A = P
=> A =
=> A =
=> A ≈ 364.996
Therefore , the solution of the given problem of percentage comes out to be the amount after 5 years is A ≈ 364.996.
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The amount after 5 years with compound interest rate is option(A) = $365. 00.
What is called interest rate?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields (APY).
Given : Principal amount : $300
rate of interest : 4% (compounded yearly)
time =5 years
Thus , to find the amount after 5 years as compounded we use , the formula:
=> A = P(1 + r/100)^t.
=> A = $300 (1 +4/100)^5
=> A = $300 (104/100)^5
=> A = $300 (1.04)^5
=> A = $300 * 1.2167
=> A = $365.00
The amount after 5 years with compound interest rate is option(A) = $365. 00.
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Please help! Due Soon - You will get 30 points and brainliest! - 4 pictures in total - links=reported - thanks!
Answer:
(the last one) i think its B
Step-by-step explanation:
Calculate the slope of the following line:
m=
Answer:
m= -1/3
Step-by-step explanation:
slope is rise/run or change in y/change in x
i pick out point (9,0) to (6,1)
the increase in y of this triangle is 1 and increase in x is 3
note that this line will have a negative slope as it goes downwards from left to right instead of upwards
hence m= rise/run= -1/3
How do you find the difference between two different numbers?
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.
Subtracting two integers from each other is a type of subtraction.
The process for determining the difference between two decimals and two whole numbers is the same.
We only add a new step.
Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.
To give them all the same amount of decimal places, we must first convert each decimal.
7.2 becomes 7.200 as a result.
The computation may now be done as before:
8.967 - 7.200 = 1.767
Therefore, there is a 1.767 discrepancy between these figures.
In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.
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Calculate the slope of the line.
m=
Answer:
m=4
Step-by-step explanation:
look at the traingle formed with line with points (6,5) and (4, -3)
look at change in y (how tall the triangle is) and change in x (the base of triangle)
change in y=8
change in x=2
m=rise/run also known as change in y/change in x
=8/2
=4
note that this is a positive gradeint line
Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
The best answer is t = 7. Option C
What is a quadratic equation?A quadratic equation is simply defined as an equation that could be rearranged in standard form.
It is also described as an algebraic equation having the highest exponent of as 2.
It is so arranged such that;
x represents an unknown valueVariables, a, b, and c represent known numbersAlso, a is not equal to 0, a ≠ 0It is important to note that the three methods of solving quadratic equation are;
FactorizationUsing the quadratic formulaUsing completing the square methodFrom the information given, we have that the form is;
x² = c
Given t squared minus 49 = 0
First, represent mathematically
t² - 49 = 0
Now, collect like terms, we have;
t² = 49
Take square root of both sides
t = √49
t = 7
Hence, the equation is t = 7
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Help please! Thank you
Answer:
the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.
2. Tell whether the segment lengths form an acute, right, or obtuse? 9, 12, 17
Answer:
obtuse angled triangle
Step-by-step explanation:
Given 3 segments , say a, b and c , with c the longest then
• If a² + b² = c² ⇒ right triangle
• If a² + b² > c² ⇒ acute triangle
• If a² + b² < c² ⇒ obtuse triangle
Here c = 17 and 17² = 289
9² + 12² = 81 + 144 = 225
Since 225 < 289 , then triangle is obtuse
Solve for x. *they are similar* NO BOTS OR ELSE U WILL BE REPORTED
Answer:
x = 5
Step-by-step explanation:
i will insert an image of my work below
Please answer!!! I’m stuck on it and need help fast <3
Find the vertex, the axis of symmetry, and the y-intercept of the graph.
Answer:
Step-by-step explanation:
Vertex (a max) is at (-3, 2).
Axis of symmetry is the vertical line x = -3.
y-intercept is (0, -1)
You can read this info directly from the illustration.
If { 4x+y=13
x−y=2
, then y=
Answer:
2.5
Step-by-step explanation:
Taking eguation i
4x+y=13
x= 13-y/4
Taking equation ii
x-y = 2
Substituting the value of x in eq i from ii
x- y =2
13-y/4- y=2
13-y-y=2×4
13-2y =8
-2y=8-13
y=-5/-2
Therefore y=2.5