Answer:
(d) x = 3 or x = 4
Step-by-step explanation:
The zero product property can be used to find the solutions to a polynomial equation when it is written in factored form.
__
Your polynomial can be put in factored form like this:
x² +12 = 7x . . . . . given
x² -7x +12 = 0 . . . . . standard form
(x -3)(x -4) = 0 . . . . . factored form*
x = 3 or x = 4 . . . . . . values of x that make the factors zero
_____
* The constants in the binomial factors must have a sum of -7 and a product of +12. It is often convenient to find them by listing factor pairs of 12:
12 = (-1)(-12) = (-2)(-6) = (-3)(-4)
Negative factors are used because we know the sum must be negative. Both have the same sign so their product is positive. The sums of the pairs shown are -13, -8, -7. The last pair is what we're looking for.
According to data from the U.S. Census Bureau, approximately 9/10 of the U.S population was less than 65 years old. What percent
of the population was less than 65?
Answer:
90%
Step-by-step explanation:
We know that 9 of 10 people were less than 65. It means, that if they would ask 100 people, the number would be 90.
The percent of population less than 65 is 90%
Ninety percent of the population was less than 65.
What is the percentage?The percentage is defined as the ratio expressed as a fraction of 100.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
According to data from the U.S. Census Bureau,
Approximately 9/10 of the U.S population was less than 65 years old.
Nine out of ten people, as far as we know, were under 65.
In other words, if they surveyed 100 persons, the answer would be 90.
Hence, Ninety percent of the population was less than 65.
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A circular flower bed is 19 m in diameter and has a circular sidewalk around it that is 4 m wide. Find
the area of the sidewalk in square meters. Use 3.14 for .
Answer:
289 m²
Step-by-step explanation:
First find the area of the flower bed
A=πr²= (3.14)(9.5)² = 283.385
Then get the area of everything including the sidewalk
A=πr²= (3.14)(13.5)² = 572.265
Then subtract and you'll get the area of just the sidewalk
572.265 - 283.385 = 288.88m²
The answer to this question is 289
2. Find m angle 1
73
88
60
80
Answer:
88
Step-by-step explanation:
angles on a straight line add up to 180
180-120=60
angles in a triangle add up to 180
60+32=92
180-92=88
angle 1=88
If f(x) = 1 / (3x – 5), what is the inverse of f?
Answer:f^-1(x) = 1/3x + 5/3
Step-by-step explanation:
Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
arc = 9π units
Step-by-step explanation:
the arc is half the circumference of the circle, then
arc = [tex]\frac{1}{2}[/tex] × 2πr = πr , then
arc = π × 9 = 9π
Answer:
[tex]\boxed{\tt 9\pi }[/tex]
Step-by-step explanation:
What we want to find here is the arc length of 1/2 of a circle, we'll start by finding the of the circle.
Step 1:- find the circumference of the circle →
[tex]\boxed{\sf Circumference\; of\; the \:circle=2\pi r}[/tex]
[tex]\tt 2\pi \times 9[/tex]
[tex]\tt 9\times 2\pi[/tex]
[tex]=\tt 18\pi[/tex]
Step 2:- find the arc length of 1/2 of the circle →
The arc length is 1/2 of the circumference of the circle:-
[tex]\boxed{\sf Circumference \; of \;\cfrac{1}{2}\; of\; the \; circle=\cfrac{1}{2}\times 18\pi}[/tex]
[tex]\tt \cfrac{18}{2} \pi[/tex]
[tex]\boxed{\tt 9\pi}[/tex]
Therefore, the arc length of the semicircle is 9π.
PLEASE HELP ME with this question
Answer:
abc are correct
Step-by-step explanation:
i took the test
In which expression is the coefficient of the n term -1?
Answer: c ???????????????????
Step-by-step explanation:
round 789 to the nearest 10
Rounding 789 nearest to tens will be 790.
Step-step Explanation:
Let's know how to round any number nearest to tens (Rules):-
We know tens place in any no. from left is at second place and number right to tens place need to be changed as:-
If last digit is 0, then we don't have to do any rounding, because it is already to the ten.We round the no. down to the nearest ten if the last digit in the no. is 1, 2, 3, or 4We round the no. up to the nearest ten if the last digit in the no. is 5, 6, 7, 8, or 9.Answer:
790
Step-by-step explanation:
PQR is a right angled triangle. The area of the triangle is 6cm² and |QR|= 3cm.
find |PR|
Answer:
PQ = 4cm
QR = 3cm
PR = 5cm
Area = 6cm²
Step-by-step explanation:
Area of triangle = 0.5 × Base × Height
6 = 0.5 × 3 × PQ
Let PQ be = x6 = 0.5 × 3 × x
[tex] \frac{6}{0.5 \times 3} = x[/tex]
x = 4cm
PQ = 4cm
Since, it is a right angled triangle applying Pythagoras Theorem,
PR =
[tex] \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{9 + 6} \\ = 5cm[/tex]
PR = 5cm
Liz leaning a total of 10 appetizers recipes over the course of 2 week of culinary school .
The number of appetizers that Liz would have learnt after 4 weeks given the unit rate is 20.
How many appetizers would Liz have learnt in 4 weeks?The first step is to determine the unit rate of appetizers that Liz learns.
Unit rate = total number of appetizers / total number of weeks
10 /2 = 5 appetizers
Number of appetizers Liz would learn in 4 weeks = 4 x 5 = 20
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Find the perimeter of the stained-glass window if each small square is 6 in. on
a side.
Answer:
the answer is B . 72√2 look at the picture I added
The cost of painting a wall that is 5 meters wide and 212 meters tall is $50. How many square meters can be painted for $1?
Answer:
21.2 square meters
Step-by-step explanation:
The area of a parallelogram is base • height.
So:
1. Calculate the area of what you can get for $50. 5 • 212 = 1060 square meters.
2. Now you divide the first price ($50) by the desired price ($1). This one is easy because 50 / 1 = 50, but I'm putting this here for future reference in case you need to solve a problem that has a desired price that's greater than $1.
3. Divide the answer to step one by the answer to step two to get the area you can have painted for $1. 1060 / 50 = 21.2 square meters.
The lens and mirror in Figure P23.51 are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. If an object is placed 1.00 m to the left of the lens, locate the final image.
The location final image from the mirror, which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.
What is the focal length of the lens?The focal length of the lens is the length of the distance between the middle of the lens to the focal point.
It can be find out using the following formula as,
[tex]-\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]
Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.
The lens and mirror in the Figure are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. Change the units of focal length in meters,
[tex]f_l=79.2\text{ cm=0.792 m}\\f_m=-50.6\text{ cm=0.506 m}[/tex]
An object is placed 1.00 m to the left of the lens. Put the value in the lens formula as,
[tex]-\dfrac{1}{v_l}+\dfrac{1}{1}=\dfrac{1}{0.792}\\-\dfrac{1}{v_l}=\dfrac{1}{0.792}-1\\v_1=3.81[/tex]
The distance of the image made by lens is 3.81 meters. The distance of this image from the mirror is,
[tex]u_2=3.81-1\\u_2=2.81\rm \; m[/tex]
This distance is work as object distance for the mirror. The focal length of mirror is -0.506 m. Thus, the location of the final image is,
[tex]-\dfrac{1}{v_2}+\dfrac{1}{3.81}=\dfrac{1}{-0.506}\\\dfrac{1}{v_2}=-\dfrac{1}{3.81}-(-\dfrac{1}{0.506})\\v_2=-0.58[/tex]
Thus, the location final image from the mirror which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.
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Which of the following values are solutions to the inequality -1 + 4x < -1?
I.4
II. 1
III. 0
Answer:
4
Step-by-step explanation:
Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid? “Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.” “Look at the graph of the relationship. Count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. Write these two numbers as a fraction.” “Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the unit rate.” “Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit rate is the difference in the corresponding x-values.” PLS HURRY
Answer:
(A) " Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
Step-by-step explanation:
1. Evaluate each expression without using a calculator.
(a) [tex](-3)^{4}[/tex]
The result of the exponential expression is 81
Indices expressionsIndices are written in term of exponents
According to the expoenent law of indices
a^4 = a * a * a * a
Given the expression
(-3)^4
This means the product of -3 in four places. Mathematically
(-3)^4 = -3 * -3 * -3 * -3
(-3)^4 = 9 * 9
(-3)^4 = 81
Hence the result of the exponential expression is 81
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tan^(2)x-tanx=0
Pls Help
Answer:
[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]
If wrong then [tex]x=-\frac{\pi }{4}.[/tex]
Step-by-step explanation:
[tex]tan^2(x)-tan(x)=0[/tex]
Factor out the tan(x).
[tex]tan(x)*(tan(x)-1)=0[/tex]
Solve for x.
[tex]tan(x)\neq 0\\[/tex] thus only option is tan(x)-1=0
[tex]tan(x)-1=0\\tan(x)=1\\[/tex]
x=tan^-1(1)⇒
Either it is Quadrant 2 or 4.
[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]
If the teacher says its wrong. Then that could only mean that its range of tan(x) is between [tex]-\frac{\pi }{2} < x < \frac{\pi }{2}[/tex] thus it's only on quadrant 4. [tex]x=-\frac{\pi }{4}[/tex]
How would I solve I need to know Asap and what is the answer
Answer:
True; True; False; True
Step-by-step explanation:
help please I'm no good at this
Here are the completed tables
Gallons Quart
1 4
2 8
5 20
7 28
Quart Pint
1 2
3 6
6 12
8 16
Pint Cup
1 2
3 6
5 10
9 18
The capacity of the objects are:
Swimming pool - 5000 gallons
Watering can - 8 quarts
Juice box - 2 pints
Soup bowl - 2 cups
The measurement from least to greatest is: 6 pints, 2 galloons, 18 cups, 6 quart.
How would the tables be filled?In order to fill the tables, the unit of conversion has to be known:
1 gallon = 4 quart
2 gallon = 2 x 4 = 8 quarts5 gallons : 5 x 4 = 20 quarts7 gallons: 7 x 4 = 28 quarts1 quart = 2 pints
6 pint / 2 = 3 quarts
12 / 2 = 6 quarts
8 x 2 = 16 pints
How to order the measurment from least to largest?
In order to order the measurement, all the measurements have to be in the same units. All the units would be converted to cups
1 quart = 4 cups
4 x 6 = 24 cups
1 galloon = 16 cups
16 x 2 = 32 cups
1 pint = 2 cups
6 x 2 = 12 cups
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Give the Least Common Denominator for
7ths, 5ths, and halves.
Answer:
7x5x2 = 70
There are no other smaller factors that include all of the given numbers
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer: correct
Step-by-step explanation theoretically it is indeed correct by acknowledging by surface+height which both angles are evenly congruent now
in terms of the 990 Degree angle i know for a fact that it corresponds with it no more to say.
pls help
The perimeter of a rectangle is 24.
Write the function that describes its area in terms of one of the sides
The perimeter of a rectangle is 24. What is the maximum possible area of such rectangle?
The perimeter of a rectangle is 24. For what length of sides does the maximum area occur for this rectangle?
The function that describes the area of the rectangle in terms of one of the sides is A = 12L - L².
How to compute the area?The perimeter of the rectangle is given as 24. Therefore, the area in terms of one of its side will be:
A = L(24 - 2L)/2
A = L(12 - L)
A = 12L - L²
The length side for the maximum area will be 6 and 6. The maximum area of the rectangle will be:
= 6 × 6
= 36
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Need help with question 15 I did the work for it but the answer was wrong somehow it didn't work out question is on the photo
Answer:
336, (B)
Step-by-step explanation:
To find the surface area, find the area of each square and triangle
10x12 + 2(6x8)/2 + 12x6 + 8x12
This would then be,
120 + 48 + 72 + 96
Surface area = 336, (B)
You made a mistake on step 2.
When finding the area of triangle, you have to divide by 2.
Hope this helps!
Help quick please!
A coin is tossed 30 times, and it comes up heads 18 times.
What is the experimental probability of tossing tails?
Answer:
0.4 or 2/5
Step-by-step explanation:
If head is 18/30, then that means that tails must be 12/30, since they must add up to one whole.
Reduce it to simplest terms: 2/5 or 0.4
please helpppp
An air conditioner manufacturer recommends that its portable units provide between 4 and 6 BTUs of cooling per cubic foot to operate most efficiently. Which statement is true?
A 16,000-BTU air conditioner meets the manufacturer recommendation for a room measuring 20 feet by 20 feet with a standard 8-foot ceiling.
A 14,000-BTU air conditioner meets the manufacturer recommendation for a room measuring 10 feet by 20 feet with a standard 8-foot ceiling.
A 20,000-BTU air conditioner will be too large for a room measuring 20 feet by 40 feet with an 8-foot ceiling.
A 12,000-BTU air conditioner will be too small for a room that is 15 feet by 10 feet with a 10-foot ceiling.
The statement is true is: A 16,000-BTU air conditioner meets the manufacturer recommendation.
Recommended BTUOption A
BTUs=16,000/(20 feet×20 feet×8 foot)
BTUs=16,000/3200 feet
BTUs=5 BTUs
Option B
BTUs=14,000/(10 feet×20 feet×8 foot)
BTUs=14,000/1600 feet
BTUs=8.75 BTUs
Option C
BTUs=20,000/(20 feet×40 feet×8 foot)
BTUs=20,000/6400 feet
BTUs=3.125 BTUs
Option D
BTUs=12,000/(15 feet×10 feet×10 foot)
BTUs=12,000/1500 feet
BTUs=8 BTUs
Based on the calculation above only option A with 5 BTUs fall between 4 and 6 BTUs.
Therefore the statement is true is: Option A.
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What is the product of x4y and 4x2
Answer:
4 x 2 (2WD) A 4x2 or 2WD is a vehicle that has a two-wheel drive (2WD) with four wheels.
Step-by-step explanation:
Mrs. Smith bought 3 pies for her family dinner. There were 10 people eating dinner. How much pie did each person get?
Answer:
Each person received 3/10 of pie
Step-by-step explanation:
3 dived by 10 equals 0.3 which is equivalent to 3/10
1 2 3 4 5 6 7 8 9 10
Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2?
StartFraction x Superscript one-half baseline Over y z squared EndFraction
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
StartFraction x z squared Over y Superscript one-half EndFraction
Using the conversion of exponent to power, the equivalent expression is given as follows:
[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]
How to transform an exponent to a power?It happens according to the following rule, with the denominator as the root and the numerator as the exponent:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
In this problem, we are given the following expression:
[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]
Negative exponents go to the denominator, hence the equivalent expression is given by:
[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]
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Please help with this questions
Answer:
16 x ^ -1/5
Step-by-step explanation:
لا
Subtract 43 from 21 raised to the 7th power, then multiply by 2.