1. What is the value of (.02)^2?
A. .4
B. .04
C. .004
D. .0004
E. .22
Answer:
D) 0.0004
Step-by-step explanation:
(0.02)^2=0.02*0.02=0.0004
Jose burns 8 calories per minute. Does Jose burn more than 500 calories per hour?
Answer: No, he burns 480
Step-by-step explanation: you multiply 8 by 60, the amount of minutes in an hour
What is the monomial if a square of a monomial is:1 9/16 a12b6
Answer:
[tex]1\dfrac{1}{4}a^6b^3[/tex]
Step-by-step explanation:
A square of a monomial is [tex]1\dfrac{9}{16}a^{12}b^6[/tex] that is [tex]\dfrac{25}{16}a^{12}b^{6}[/tex]
Use properties of exponents:
[tex](a^m)^n=a^{mn}\\ \\\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m\\ \\a^mb^m=(ab)^m[/tex]
Note that
[tex]\dfrac{25}{16}=\dfrac{5^2}{4^2}=\left(\dfrac{5}{4}\right)^2\\ \\a^{12}=a^{6\cdot 2}=(a^6)^2\\ \\b^6=b^{3\cdot 2}=(b^3)^2[/tex]
Then
[tex]\dfrac{25}{16}a^{12}b^{6}=\left(\dfrac{5}{4}\right)^2\cdot (a^6)^2\cdot (b^{3})^2=\left(\dfrac{5}{4}a^6b^3\right)^2[/tex]
So, the monomial is
[tex]\dfrac{5}{4}a^6b^3=1\dfrac{1}{4}a^6b^3[/tex]
Anybody know how to do this?
Step-by-step explanation:
When a factor appears in both the numerator and denominator, that is a hole in the function.
Therefore, the domain of h(x) is (-∞, 4) (4, ∞).
Which means the range of h(x) is (-∞, 5) (5, ∞).
Graph: desmos.com/calculator/j58gdgugxy
Which quantity is best modeled by a linear function
See the explanation
Explanation:Since you haven't provided any options I'll face this problem in a general way. Linear functions are given of the form:
[tex]y=mx+b[/tex]
This is called the slope-intercept form of the equation of a line. When modeling a linear function we need to take into account that we will have a constant rate of change and that when plotting our model this will follow a line. In order to model a problem as a linear function we need to follow some tips:
Identify the changing quantities in order to define the variables that stands for them.Draw a diagram or a coordinate system. It is usual to use the Cartesian coordinate system.Read the problem in detail.Set a mathematical model writing the equation that stands for the problem.Set values into the variables in order to check your model.Check your results.Learn more:Linear function: https://brainly.com/question/13768783
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The quantity that is best modeled by a linear function must fit into y = mx + c
A model is a representation of reality. There are many different types of models such as;
Mathematical modelsComputer modelsGraphic modelsA linear function is a function of the sort y =mx + c. The quantity is not shown in the question hence the question is incomplete.
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If the dimensions of the foundation on the blueprint are 11 inches by 13 inches, what are the actual
dimensions in feet?
Does the addition problem show a way to add 27 + 38?
Circle Yes or No for each addition problem.
a. 20 + 7 + 30 + 8 Yes No
b. 20 + 70 + 38 yes no
c. 20 + 30 + 7 + 8 Yes No
d. 50 + 10 + 5 yes no
Answer:
a. yes
b. no
c. yes
d. yes
Step-by-step explanation:
For a, 27 + 38 can be broken apart. 27 is broken up by adding smaller numbers (20 + 7 = 27) and the same is done with 38 (30 + 8 = 38), so A and C shows a way to add 27 and 38. In C, the numbers are just put into a different order. B is not a way to add 27 and 38, because the sum is different.
27 + 38 = 65, however 20 + 70 + 38 = 128. The addition problem for D is a way to solve for 27 + 38, because it is broken up differently than A and C. They instead added the 20 and 30 together first, then split up 15 (from 8+7) into 10 and 5. So D is a way to solve, because it gets the same answer as 27 and 38 :D
A trapezoid has coordinates of (-5, -3), (-2, 5), (2, 5), and (5, -3). What is the approximate perimeter of the trapezoid?
Round your answer to the nearest whole number (number that is not a decimal).
Answer:
The approximate perimeter of the trapezoid is 31 units
Step-by-step explanation:
step 1
Plot the trapezoid
Let
A(-5, -3), B(-2, 5), C(2, 5), and D(5, -3)
see the attached figure
step 2
Find the perimeter of trapezoid
we know that
The perimeter of trapezoid is equal to
[tex]P=AB+BC+CD+AD[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
we have
[tex]A(-5, -3),B(-2, 5)[/tex]
substitute in the formula
[tex]d=\sqrt{(5+3)^{2}+(-2+5)^{2}}[/tex]
[tex]d=\sqrt{(8)^{2}+(3)^{2}}[/tex]
[tex]d_A_B=\sqrt{73}\ units[/tex]
Find the distance BC
we have
[tex]B(-2, 5),C(2, 5)[/tex]
substitute in the formula
[tex]d=\sqrt{(5-5)^{2}+(2+2)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]d_B_C=4\ units[/tex]
Find the distance CD
we have
[tex]C(2, 5),D(5, -3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-5)^{2}+(5-2)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(3)^{2}}[/tex]
[tex]d_C_D=\sqrt{73}\ units[/tex]
Find the distance AD
we have
[tex]A(-5, -3),D(5, -3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3+3)^{2}+(5+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(10)^{2}}[/tex]
[tex]d_A_D=10\ units[/tex]
step 3
Find the perimeter
[tex]P=AB+BC+CD+AD[/tex]
substitute the values
[tex]P=\sqrt{73}+4+\sqrt{73}+10[/tex]
[tex]P=31\ units[/tex]
√5 • √80
Please answer and show your steps.
√5 • √80
Combine the two using the product rule for radicals:
√(5 • 80)
Multiply:
√400
Rewrite 400 as 20^2
√20^2
= 20
The answer is 20
Find the height of the image after it has been scaled by 80% the following number of times. Explain or show your reasoning
After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.
To find the height of the image after it has been scaled by 80% multiple times, we can use the formula for scaling:
[tex]\[ \text{New height} = \text{Original height} \times (\text{Scale factor})^{\text{Number of times scaled}} \][/tex]
Given that the original height is 150 mm and the scale factor is 80% (or 0.8), we can calculate:
a. After being scaled 3 times:
[tex]\[ \text{New height} = 150 \times (0.8)^3 = 150 \times 0.512 = 76.8 \, \text{mm} \][/tex]
b. After being scaled 6 times:
[tex]\[ \text{New height} = 150 \times (0.8)^6 = 150 \times 0.262 \approx 39.3 \, \text{mm} \][/tex]
As the image is scaled down by 80% each time, its height decreases significantly with each iteration.
After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.
These heights fall within the acceptable range for a U.S. passport photo (25-35 mm).
The probable question may be:
The distance from Elena's chin to the top of her head is 150 mm in an image. For a U.S. passport photo, this measurement needs to be between 25 mm and 35 mm. PASSPORT PHOTO 1. Find the height of the image after it has been scaled by 80% the following number of times. Explain or show your reasoning. a. 3 times b. 6 times
How do you solve the equation x over 4 +2 = -12
For this case we must solve the following equation:
[tex]\frac {x} {4} + 2 = -12[/tex]
Subtracting 2 from both sides of the equation we have:
[tex]\frac {x} {4} = - 12-2[/tex]
Equal signs are added and the same sign is placed.
[tex]\frac {x} {4} = - 14[/tex]
Multiplying by 4 on both sides of the equation we have:
[tex]x = -14 * 4\\x = -56[/tex]
Thus, the solution of the equation is [tex]x = -56[/tex]
Answer:
[tex]x = -56[/tex]
Solve the equation x over 2 =6
Answer: 12
Step-by-step explanation: To solve this equation, since x is being divided by 2, in order to get x by itself, we need to multiply by 2 on both sides of the equation.
On the left side of the equation, the 2's cancel and we have x and on the right side of the equation, 6 × 2 gives us 12 so we have x = 12 which is the solution for our equation.
To check our solution, we plug 12 in for x in the original equation.
Image provided.
A pilot is traveling at a height of 30,000 feet above ground she looks down at a angle of depression of 6 and spots runway as measured along the ground how many miles away is she from the runway
Distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.
Solution:Given that
Height of position of pilot from the ground = 30000 feet
Angle of depression when he looks down at runway = 6o
Need to measure along the ground, distance between runway and pilot that is horizontal distance between runway and pilot.
Consider the figure attached below
D represents position of runway.
P represents position of pilot.
PG represents height of position of pilot from the ground that means PG = 30000 feet
PH is virtual horizontal line and HPD is angle of depression means ∠ HPD = 6 degree
AS DG and HP are horizontals, so DG is parallel to HP.
=> ∠ HPD =∠ PDG = 6 degree [ Alternate interior angle made by transversal PD of two parallel lines ]
We need to calculate DG
Consider right angles triangle PGD right angles at G
[tex]\text {As } \tan x=\frac{\text { Perpendicular }}{\text { Base }}[/tex]
[tex]\tan \angle \mathrm{PDG}=\frac{\mathrm{PG}}{\mathrm{GD}}[/tex]
[tex]\begin{array}{l}{=>\mathrm{GD}=\frac{\mathrm{PG}}{\tan \angle \mathrm{PDG}}} \\\\ {=>\mathrm{GD}=\frac{30000}{\tan 6^{\circ}}=285430.9336}\end{array}[/tex]
As one foot = 0.000189 miles
[tex]=>285430.9336 \text { feet }=285430.9336 \times 0.000189 \text { miles }=53.9464 \text { miles. }[/tex]
Hence distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.
Final answer:
To find the distance to the runway, we can use trigonometry and create a right triangle using the pilot's height and the angle of depression. Using the tangent function, we can solve for the distance. The pilot is approximately 58.47 miles away from the runway.
Explanation:
To find the distance to the runway, we can use trigonometry. The angle of depression of 6 degrees tells us that the runway is below the pilot's line of sight. We can create a right triangle with the pilot's height of 30,000 feet as the opposite side and the distance to the runway as the adjacent side. Using the tangent function, we can solve for the distance:
Tan(6) = Opposite/Adjacent
Tan(6) = 30,000/Adjacent
Adjacent = 30,000/Tan(6)
Using a calculator, we find that the pilot is approximately 308,517 feet away from the runway.
To convert this distance to miles, we divide by 5,280 (since there are 5,280 feet in a mile):
308,517/5,280 ≈ 58.47 miles
Therefore, the pilot is approximately 58.47 miles away from the runway.
Which is the Best Buy?
Whole wheat weighs 16oz and costs $2.24
Pita weighs 20oz and costs $3.60
7-grain weighs 16oz and costs $2.56
Which is the Best Buy?
Answer:whole wheat
Step-by-step explanation:
Its whole wheat because when you divide the cost by the weight whole wheat is the best deal
distance=100km, time=75 minutes, speed=?
Step-by-step explanation:
speed= distance/time
time is meant to be in seconds
1mins = 60 secs
75mins =75 x 60 = 4500
distance is meant to be in metres
1metre= 0.001km
100 km = 100 x 1000= 100000
speed =distance/time
speed = 100000/4500
speed=22.22m/s
Answer:
[tex]\large\boxed{80\dfrac{km}{h}}[/tex]
Step-by-step explanation:
[tex]speed=\dfrac{distance}{times}\\\\\text{We have:}\\\\distance=100km,\ time=75min\\\\1h=60min\to1min=\dfrac{1}{60}h\\\\time=\dfrac{75}{60}h=\dfrac{5}{4}h=1.25h\\\\\text{Substitute:}\\\\speed=\dfrac{100km}{1.25h}=80\dfrac{km}{h}[/tex]
PLEASE HELP!I'M NEWW
Answer:
I think its 90°, since it l00ks like a right angle
TRANSLATE INTO AN INEQUALITY!!
seven subtracted from c is less than -30
Answer:
7-c < 30
Step-by-step explanation:
its in your question.
Steve and carol live 405 miles apart, they start at the same time and travel toward each other, Steve speed is 6mph greater than carols. If they meet in 2.5 hours, find their speed
Answer:
Speed of Carol is 78 mph and that of Steve is 84 mph.
Step-by-step explanation:
Let the speed of Carol is x mph and that of Steve is (x + 6) mph.
If they move towards each other with that speed, then the resultant speed will be (x + x + 6) = (2x + 6) mph
With this resultant speed, they cover 405 miles in 2.5 hours.
So, [tex]2x + 6 = \frac{405}{2.5} = 162[/tex]
⇒ 2x = 156
⇒ x = 78 mph
So, speed of Carol is 78 mph and that of Steve is (78 + 6) = 84 mph. (Answer)
Cory is paid $567.20 biweekly.
What is his annual salary?
O
$6,806.40
$13,612.80
o
$14,747.20
$29,494.40
Answer:
14,747.20
There are 52 weeks in a year being paid bi-weekly means being paid every other week or 26 times a year. So 567.20 * 26 is 14747.20.
PLEASE HELP ME me me me
Answer:
Andre has the correct answer. When simplified his answer is equivalent to the original equation.
Answer:
2pg1
Step-by-step explanation:
Hehe
Danny's Diner sold 60 milkshakes last week. 10% of the milkshakes had whipped cream on
top. How many milkshakes with whipped cream were sold?
milkshakes
Answer:
6
Step-by-step explanation:
it's asking how much makes 10% of 60 and to find it we use this formula :
60 ÷ 100 × 10 = 6
Answer:
6 milkshakes
Step-by-step explanation:
All you need to do is multiply:
60 (0.10) = 6
A rectangular swimming pool is 21 metres
wide and 50 metres long. Calculate the length
of the diagonal to 1 decimal place.
Answer:
The length of the diagonal measures 54.2 meters
Step-by-step explanation:
Pythagorean theorem,
a² + b² = c²
a = 21
b = 50
c = diagonal
21² + 50² = c²
441 + 2500 = c²
2941 = c²
√2941 = c
54.23098... = c
54.2 = c
The length of the diagonal measures 54.2 meters.
We have given that,
A rectangular swimming pool is 21 meters
wide and 50 meters long.
We have to determine the length of the diagonal.
What is the Pythagorean theorem?a² + b² = c²
a and b are sides of the triangle and c is the hypotenuse
a = 21,
b = 50
c = diagonal
21² + 50² = c²
441 + 2500 = c²
2941 = c²
Taking square root on both side
√2941 = c
54.23098 = c
54.2 = c
Therefore the length of the diagonal measures 54.2 meters.
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Simplify each expression.
1) -8(k - 4)
Answer:
-8(k - 4) = -8k + 32Step-by-step explanation:
-8(k - 4) use the distributive property: a(b + c) = ab + ac
= (-8)(k) + (-8)(-4) = -8k + 32
Answer:
-8k+32
Step-by-step explanation:
-8(k-4)=-8k+32
Question 9 of 15 (1 point)
4.4 Section Exercise 15
Use the problem-solving flowchart.
The sum of four times a number and ten is equal to the difference of the number and seventeen.
Find the number. Round your answer to the nearest integer, if necessary.
As
The number is
The number is -9
Step-by-step explanation:
Let x be the number then according to given statement
[tex]4x+10 = x-17[/tex]
Subtracting 10 from both sides
[tex]4x+10-10 = x-17-10\\4x = x-27[/tex]
Subtracting x from both sides
[tex]4x-x = x-x-27\\3x = -27[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} = \frac{-27}{3}\\ x = -9[/tex]
Verification:
[tex]4(-9)+10 = -9-17\\-36+10=-26\\-26=-26[/tex]
The number is -9
Keywords: Linear equation, variables
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If sin (2x+7)= cos(4x-7), what is the value of x
Answer: 15
Step-by-step explanation:
Recall : if sin α = cos β , then α + β are complementary , that is
α + β = 90
Since sin (2x+7) = cos(4x-7) , then (2x+7) and (4x-7) are complementary , that is:
2x + 7 + 4x - 7 = 90
6x = 90
x = 90/6
x = 15
The missing value x is constituting the angles of both sin and cos trigonometric ratios.
By using complementary property, the value of x for given condition is evaluated as 15.
Given that:sin(2x + 7) = cos(4x - 7)Explanation and calculations for value of x:The missing value x is constituting the angles of both sin and cos trigonometric ratios.
Its known by trigonometry that when [tex]sin(\alpha) = cos(\beta)[/tex], then [tex]\alpha + \beta = 90^{\circ}[/tex]
Thus, we have:
[tex]2x + 7 + 4x - 7 = 90\\\\6x = 90\\\\x = \dfrac{90}{6}\\\\x = 15[/tex]
Thus, value of x for given condition is 15.
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Solve for x.
24 =-11x-8+ 3x
Answer:
-4 = x
Explanation:
-11x +3x =-8x
24=-8x-8
+8= +8
--------------
32=-8x
--- -----
-8. -8
x= -4
To solve for x in the equation 24 =-11x-8+ 3x, combine like terms and isolate the variable by performing algebraic operations.
Explanation:To solve for x in the equation 24 =-11x-8+ 3x, we can combine like terms:
24 = -11x + 3x - 824 = -8x - 8Add 8 to both sides to isolate the variable:24 + 8 = -8x - 8 + 832 = -8xDivide both sides by -8 to solve for x:x = 32 / -8x = -4Therefore, the solution for x is -4.
The temperature of the ice for an ice hockey match is -7°C. For ice-skating, the temperature of the ice is 2 degrees warmer. What is the temperature of ice for ice-skating?
Answer:
Temperature of the ice for ice-skating = -5 °C
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Temperature of the ice for an ice hockey match = - 7 °C
Temperature for ice- skating is 2 degrees warmer.
2. What is the temperature of the ice for ice-skating?
For the correct calculation, we use this formula:
Temperature for ice-skating = Temperature of the ice for a hockey match + 2
Temperature for ice-skating = -7 + 2
Temperature of the ice for ice-skating = -5 °C
We add 2 to the temperature of the ice for a hockey match because the temperature for ice-skating is described as warmer. If it were described as colder, we should subtract.
Answer:
-5c
Step-by-step explanation:
because basically you subtract because it is below normal
5. An $800 deposit for 24
months earned $200 in
interest
Answer:
The rate of interest applied fro compound interest is 24.5 %
The rate of interest applied simple interest is 37.5 %
Step-by-step explanation:
Given as :
The Principal amount that is deposited = $ 800
The Time period = 24 months = 2 years
The Interest earn = $ 200
Let the rate of interest = R %
So, The Amount = Principal deposited - interest earn
Or, A = $ 800 - $ 200
∴ Amount = $ 600
From compounded method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]
Or, $ 600 = $ 200 × [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]
Or, [tex]\frac{600}{200}[/tex] = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]
Or, 3 = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]
Or, [tex]3^{\frac{1}{2}}[/tex] = (1 +[tex]\frac{R}{100}[/tex])
Or, 1.245 = (1 +[tex]\frac{R}{100}[/tex])
or, 1.245 - 1 = [tex]\dfrac{R}{100}[/tex]
or, 0.245 × 100 = R
So, the rate is = 24.5 %
Hence The rate of interest applied fro compound interest is 24.5 % Answer
From Simple Interest method
Simple Interest = [tex]\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}[/tex]
Or, $ 600 = [tex]\dfrac{\textrm 800\times \textrm R\times \textrm 2}{100}[/tex]
Or, $ 600 × 100 = $ 800 × R × 2
Or, R = [tex]\frac{60000}{1600}[/tex]
∴ R = 37.5 %
So, The rate is 37.5 %
Hence The rate of interest applied simple interest is 37.5 %Answer
what is the area of a rectangle with a length of 3ft and a width of 16.1 ft
The sum of three times a number and -4 is at least twice the number plus 8 as an inequality
Final answer:
To translate the given statement into an inequality, it converts to 3x - 4 ≥ 2x + 8. Through simplification, we find that x must be at least 12. This showcases the application of basic algebra rules and solving inequalities.
Explanation:
The question asks to translate 'The sum of three times a number and -4 is at least twice the number plus 8' into an inequality. This can be put into mathematical terms as 3x - 4 ≥ 2x + 8, where 'x' represents the unknown number. To solve, we follow several steps:
Subtract 2x from both sides, resulting in x - 4 ≥ 8.
Add 4 to both sides to isolate the variable, giving x ≥ 12.
This inequality tells us that for the original statement to hold true, the number (x) must be 12 or greater. The process involves understanding operations with numbers, such as adding, subtracting, and applying the rules of inequality to solve for 'x'.