Answer:
11
Step-by-step explanation:
24.75 / 2.25 = 11
The width of a rectangle is the length minus 3 units. The area of the rectangle is 40 units. What is the width, in unit, of the rectangle?
Answer: The width is 5
Step-by-step explanation:
The equation is x*(x-3)=40 solviing for x which is 8 but since width is x-3 then 8-3=5
Carter is going to invest $210 and leave it in an account for 5 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Carter to end up with $250?
Answer:360
Step-by-step explanation:g-g5
The rate of interest will be 0.35.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula[tex]CI = P(1+\frac{r}{n}) ^{nt} -P[/tex]
and, the Amount is given by
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A is amount
P is principal
r is rate of interest
n is number of times interest is compounded per year
t is time
According to the given question
Principal, P = $210
Amount, A = $250
Time, t = 5 years
n = 1
Therefore, the interest rate is given by
Amount = [tex]P(1+\frac{r}{n}) ^{nt}[/tex]
⇒[tex]250 = 210(1+\frac{r}{1}) ^{5}[/tex]
⇒[tex]\frac{250}{210} =(1+r)^{5}[/tex]
⇒[tex]1.19 = (1+r)^{5}[/tex]
⇒[tex]\sqrt[5]{1.19} = 1+r\\[/tex]
⇒ 1.035 = 1 + r
⇒ r = 1.035 - 1
⇒ r = 0.35
Hence, the interest rate is o.35.
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When Mohammed was born, the baby was 21 inches tall. at his last check up, he was 38 inches tall. what is the percent increase in his growth to the nearest percent? round it to the nearest 100th
this is math btw and im giving 5 star and 15 points.
Answer:
80.95
Step-by-step explanation:
Percentage increase = [tex]\frac{New Value - Old Value}{Old Value}[/tex] *100
=> (38-21)* 100/21 = 80.9523%
The answer round it to the nearest 100th = 80.95%
A U.S. penny has a mass of 2.5 grams. A U.S. quarter has a mass of 5.67 grams. What is the total mass of the two coins?
A car salesman receives 3% commission on his total weekly sales. Last week his total sales were £28500
How much commission does he earn?
Find the length of x.
Answer:
5
Step-by-step explanation:
6/4 = 7.5/x
7.5/1.5=5
What do you get when you plug 4 in the following function?
Answer:
567
Step-by-step explanation:
It will become:
y = 7(3)^4
y = 7 * 81
y = 576
Answer:
Y = 567
Step-by-step explanation:
Y=7(3)(3)(3)(3)
Kim spent $44 on eating utensils. Spoons cost $4 and forks cost $6. If she bought a total of 9 utensils then how many of each kind did she buy?
Answer:
3 spoons and 6 forks
Step-by-step explanation:
9 = x + y; x= 9-y
44 = 4x + 6y
44 = 4(9-y) + 6y
44 = 36 - 4y +6y
44 = 36 +2y
2y = 44-36 = 12
y = 12/2 =6
x= 9-y = 9-6 =3
Find the product.
10(-7)
Answer:
-70
Step-by-step explanation:
If a number is right by a parathesis () then you multiply the number inside the parathesis by the number next to them.
There are 39 students in a class.
16 of the students are female. Find the percentage of the class that are female.
Give your answer to the nearest percent.
An 11-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 14 m. Find the length of the shadow. If necessary,
round your answer to the nearest tenth.
14
11
?
Answer:
8.66 m
Step-by-step explanation:
Given that,
The distance from the top of the building to the tip of the shadow is 14 m
The height of the building is 11 m.
We need to find the length of the shadow. we can see that the length of the shadow forms the base of the triangle.
The distance from the top of the building to the tip of the shadow form hypotensue and height of the building forms perpendicular. So, we can use Pythagoras theorem to find the base.
So,
[tex]H^2=b^2+h^2\\\\b^2=H^2-h^2\\\\b=\sqrt{14^{2}-11^{2}}\\\\b=8.66\ m[/tex]
So, the length of the shadow is 8.66 m.
Solve the formula for t.
d= rt
Determine if each of the numbers below is a solution to the inequality 3x-2<2-2x. SHOW ALL OF YOUR WORK
a. 2
b. 1/2
c. -3
d. 2/3
Answer:
b, c, and d are solutions
Step-by-step explanation:
3x - 2 < 2 - 2x
5x - 2 < 2
5x < 4
x < 4/5
b) 1/2 < 4/5 true
c) -3 < 4/5 true
d) 2/3 < 4/5 true
15 pints because 2 questions
Answer:
1.its B
2.G
Step-by-step explanation:
can you help me please
Answer:
25/6
Step-by-step explanation:
Evaluate the expression.
–3×(6– -6÷3)
PLEASE HELP
-24 i hope this is right
Answer:
−24
Steps for answer:
1. Simplify 6÷3 to 2.
−3×(6+2)
2. Simplify 6+2 to 8.
−3×8
3. Simplify
−24
Find the value of each variable and the measure of each labeled angle (2x) (3x-42)
Step-by-step explanation:
Head opposite angles
2x= 3x-42
x= 42°
the angles are 84°
Each of the pairs of opposite angles made by two intersecting lines is called a pair of vertical angles. The value of x is 42 and the measure of the two given angles is 84° each.
What are vertical angles?Each of the pairs of opposite angles made by two intersecting lines is called a pair of vertical angles.
The two of the given angles are vertically opposite angles, therefore, the measure of the two given angles will be the same.
(2x)° = (3x - 42)°
2x = 3x - 42
Subtract 2x from both sides of the equation and add 42 to both sides of the equation,
2x - 2x + 42 = 3x - 42 - 2x + 42
42 = 3x - 2x - 42 + 42
42 = x
Therefore, the value of x is 42. Now, the measure of each angle can be written as,
(2x)° = 2(42) = 84°
(3x - 42)° = 3(42) - 42 = 84°
Hence, the value of x is 42 and the measure of the two given angles is 84° each.
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Write an equation in slope-Intercept form from the polnts (-4,-2) and (-3,5)
y = 1/7x
y = 1/7x + 26
y = 7x + 26
x = 7y + 26
Answer:
y=7x+26
Step-by-step explanation:
First we have to find the slope of the lines.
(-4,-2)
(-3,5)
Our slope is going to equal 7
then we take a point and use it to find the equation
y--2=7(x--4)
y+2=7x+28
y=7x+26
HELP PLEASE CHECK MY ANSWER!!!
Answer:
its almost correct but its just a little bit off
Step-by-step explanation:
1. on the left its on the two bring it closer to the 4 than the 2 so its gonna be right before the four ill insert a picture so u can see as well.
2. on the left side its going to be right before -2.
3. on the bottom its going to be moved down to -18 and a little bit out going to the right.
the picture is right there hope it helped
The sales tax in your city is 8.8 and an item costs $63 before tax.
How much tax would you pay on that item?
Round to the nearest hundredth or cent.
The diameter of a circl
10. d = 6.7 in.
Find the area of the triangle
19cm
15cm
12cm
Answer:
Step-by-step explanation:
I need help with this. Please!
911÷406 con operaciones
Answer:
2.24384236453
Step-by-step explanation:
division/división
Answer:
Step-by-step explanation:
2.24384236453 divicion y divicion
Which pairs of equations are parallel?
a) y = 3x + 4 and y = 3x+1
b) y =- 3x + 4 and y = 3x + 1
c) y=x-1 and y = x+1
d) y = 2x + 3 and y = 2x + 1
Answer:
x by 1 times 15 to the third power
Step-by-step explanation:
eighteen is equal to the product of a number (n) and 9
eighteen is equal to the product of a number 9 and 9
(3z+1)+5+7z) Step by step explanation needed
Answer: 10z + 6
Step-by-step explanation:
this is a short problem.. sometimes you would need to distribute, but since there is no number in front of parenthesis you can just get rid of them
that gives you: 3z + 1 +5 + 7z
now from here we combined liked terms
7z + 3z = 10z
1 + 5 = 6
so that gives you: 10z + 6
2/5 divided by 4 and reduce the answer
Answer:
1/10 i guess
Step-by-step explanation:
2/5=0.4
0.4/4=0.1
0.1=1/10 (one tenth_
Answer:
1/10
Step-by-step explanation:
2/5 ÷4 is the same as 2/20, which is 1/10
HELP ME PLZ !!! IT'S ALGEBRA
Answer:
x = - 8/23
y = 40/23
Step-by-step explanation:
-5x- y = 0
and
-8x+3y = 8
The first step to solve this would be to get what one of the two variables equal. The easiest in this case is y from the first equation.
-5x-y = 0
-y = 5x
y = - 5x
Now you can take this y value and plug it into the section equation.
-8x + 3(-5x) = 8
-8x - 15x = 8
-23x = 8
x = - (8/23)
Once you get the x value you can plug it back into equation one to get y's value
-5*-(8/23) - y = 0
40/23 - y = 0
y = 40/23
Use the limit definition of the derivative to find the slope of the tangent line to the curve
f(x)= 7x^2 + 7x + 3 at x= 4
Answer:
[tex]\displaystyle f'(4) = 63[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Expand by FOIL (First Outside Inside Last)FactoringFunction NotationTerms/CoefficientsCalculus
Derivatives
The definition of a derivative is the slope of the tangent line.
Limit Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = 7x² + 7x + 3
Slope of tangent line at x = 4
Step 2: Differentiate
Substitute in function [Limit Definition of a Derivative]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x + h)^2 + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Expand [FOIL]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x^2 + 2xh + h^2) + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Distribute: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7x^2 + 14xh + 7h^2 + 7x + 7h + 3] - 7x^2 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x²): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7x + 7h + 3 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h + 3 - 3}{h}[/tex][Limit - Fraction] Combine like terms: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h}{h}[/tex][Limit - Fraction] Factor: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{h(14x + 7h + 7)}{h}[/tex][Limit - Fraction] Simplify: [tex]\displaystyle f'(x)= \lim_{h \to 0} 14x + 7h + 7[/tex][Limit] Evaluate: [tex]\displaystyle f'(x) = 14x + 7[/tex]Step 3: Find Slope
Substitute in x: [tex]\displaystyle f'(4) = 14(4) + 7[/tex]Multiply: [tex]\displaystyle f'(4) = 56 + 7[/tex]Add: [tex]\displaystyle f'(4) = 63[/tex]This means that the slope of the tangent line at x = 4 is equal to 63.
Hope this helps!
Topic: Calculus AB/1
Unit: Chapter 2 - Definition of a Derivative
(College Calculus 10e)
