Answer:
40,000 ft
Step-by-step explanation:
The area of a rectangle is weight*length, and the perimeter is the sum og the four sides, which are 2 lengths sides ans 2 width sides, so:
area = w*l
perimeter = 2w + 2l
If the perimeter is 1000 ft:
2w + 2l = 1000
Also, the length is 300 ft more than width, so:
l = 300 +w
So, our system is:
2w + 2l = 1000 (equation 1)
l =300 + w (equation 2)
Son, we can solve it by replacing equation 2 in equation 1:
2w + 2(300 +w) = 2w + 600 + 2w = 4w + 600 = 1000
Now, subtract 600 in both sides:
4w + 600 - 600 = 1000 - 600
4w = 400
Divide both sides by 4:
4w/4 = 400/4
w = 100
Lets replace this w value in equation 2 to find l:
l = 300 + 100 = 400, so l=400
Finally we can find the area using the area formula:
area = 400*100 = 40,000 ft2
So, the area is 40,000 ft2
Final answer:
The area of the pasture is found by setting up and solving a linear system (1000 = 2w + 2(w + 300)); the dimensions of the rectangle are found to be 100 feet in width and 400 feet in length. The area is then calculated by multiplying the width by the length, yielding an area of 40,000 square feet.
Explanation:
To solve the problem, we need to establish a system of linear equations to find the dimensions of the pasture. Given that the perimeter of a rectangle is 2 times the width plus 2 times the length (P = 2w + 2l), and the length is 300 feet more than its width (l = w + 300), we can set up the following equations:
P = 2w + 2l
l = w + 300
Since we know the perimeter is 1000 feet, we substitute this value into the first equation:
1000 = 2w + 2(w + 300)
1000 = 2w + 2w + 600
1000 = 4w + 600
400 = 4w
w = 100 feet
Once we have the width, we can substitute this into the second equation to find the length (l):
l = 100 + 300
l = 400 feet
To find the area of the pasture, we multiply the width by the length:
Area = width × length = 100 feet × 400 feet = 40,000 square feet
The area of the pasture is 40,000 square feet.
simplest form of 8/10
Answer:
a.3/4 b.2/3
Step-by-step explanation:
Answer:
a) 3/4
b) 2/3
Step-by-step explanation:
a) 15 ÷ 5 3
_________ = ____
20 ÷ 5 4
b) 8 ÷ 4 2
_________ = ____
12 ÷ 4 3
Hope this helps OwO!
In 2015, nearly three out of every ten autos sold in a country was a crossover utility vehicle. If an auto dealership sold 4800 vehicles in total that year, how many of these sales would be expected to involve a cuv? Simplify your answer.
Answer:
about 160
Step-by-step explanation:
Answer:
1440 CUVs, approx. Actual number would be slightly lower.
Step-by-step explanation:
To answer this question, multiply 4800 vehicles by (3/10) for an approximation of the number of CUVs sold:
4800 3
---------- * ------- = 1440 CUVs
1 10
Ramon earns $1,825 each month and pays $53.20 on electricity. To the nearest tenth of a percent, what
percent of Ramon's earnings are spent on electricity each month?
Answer:
2.9%
Step-by-step explanation:
Given:
Total earnings : $1,825
Electricity : $53.20
% of earnings spent on electricity,
= (53.2 / 1825) x 100%
= 0.2915 x 100%
= 2.915%
= 2.9% (nearest tenth)
In the spinner below the large wedges are twice the size of the smaller ones. What is true about the probability of landing on 6 and the probability of landing on 5?
Answer:
A
Step-by-step explanation:
If we take each small section to be "1" unit, we can say the large sections (for "2" and "5") are "2" units each. So in total there will be 8 sections.
Since 5 is "2" sections, we can say:
P(5) = 2/8 = 1/4
And 6 is "1" section, so we can say:
P(6) = 1/8
Definitely, Probability of landing a 6 is HALF that of probability of landing a 5. Also we can see this is the picture.
So, from the answer choices, A is right.
For each sequence,find the first 4 terms and the 10th term
a) n+5
b)2n-1
Answer:
a)6,7,8,9 and 10th term is 15.
b)1,3,5,7 and 10th term is 19.
Step-by-step explanation:
Given a) n+5
b)2n-1
Solution for a) n+5
Taking the value of n is 1 we get the first term of the sequence;
[tex]n+5=1+5=6[/tex]
Similarly taking the value of n 2,3,4 we get;
[tex]2+5=7\\3+5=8\\4+5=9[/tex]
And for 10th term we take the value of n is 10 and get;
[tex]n+5=10+5=15[/tex]
So the solution for 1st sequence is 6,7,8,9 and 10th term is 15.
Solution for b)2n-1
Taking the value of n is 1 we get the first term of the sequence;
[tex]2n-1=2\times1-1=2-1=1[/tex]
Similarly taking the value of n 2,3,4 we get;
[tex]2n-1=2\times2-1=4-1=3\\2\times3-1=6-1=5\\2\times4-1=8-1=7[/tex]
And for 10th term we take the value of n is 10 and get;
[tex]2n-1=2\times10-1=20-1=19[/tex]
So the solution for 2nd sequence is 1,3,5,7 and 10th term is 19.
Final answer:
The first 4 terms and the 10th term of sequence (a) n + 5 are 6, 7, 8, 9, and 15, respectively. For sequence (b) 2n - 1, they are 1, 3, 5, 7, and 19, respectively.
Explanation:
For each sequence, we need to find the first 4 terms and the 10th term. The sequences are given by (a) n + 5 and (b) 2n - 1.
Let's start with sequence (a) n + 5. The first 4 terms, where n starts at 1, will be:
1 + 5 = 62 + 5 = 73 + 5 = 84 + 5 = 9The 10th term can be found by substituting n = 10 into the expression, so the 10th term is:
10 + 5 = 15
Moving on to sequence (b) 2n - 1. The first 4 terms are:
2(1) - 1 = 12(2) - 1 = 32(3) - 1 = 52(4) - 1 = 7The 10th term is calculated as:
2(10) - 1 = 19
I need help with these 2 Math Questions, both using a graph. Pictures are attached.
Answer:
1. k = 3
2. k = 5
Step-by-step explanation:
1. The graph shows two parallel lines intersecting y-axis:
f(x) at (0,2);g(x) at (0,5).The graph of the function g(x) is translated 5 - 2 = 3 units up graph of the function f(x). Thus, k = 3.
2. The graph shows two parallel lines intersecting y-axis:
f(x) at (0,-2);g(x) at (0,3).The graph of the function g(x) is translated 3 - (-2) = 5 units up graph of the function f(x). Thus, k = 5.
Complete each geometric sequence
1.5, 3, 6, ___, 24, ___
Answer:
1.5, 3, 6, 12, 24, 48
Explanation:
multiply all of the numbers by 2
1.5*2=3
3*2=6
6*2=12
12*2=24
24*2=48
Which answer describes the 2X in the expression 2x+4
Answer:
2 is a co-efficient to the variable, x. 4 is a constant.
Step-by-step explanation:
Don't know exactly what you're asking here.
6. Museum tickets cost $7 for
adults and $4 for youths. The
museum is free for anyone
5 years and younger. The Baker
family is planning to visit with
7 adults, 6 youths, and
3 children under the age of 5.
How much will all of their tickets
cost? Explain.
Answer:
$73
Step-by-step explanation:
Multiply 7 and 7 to get 49. Next, multiply 6 and 4 to get 24. The museum is free for the 3 children so you do not have to do anything. Add 49 and 24 to get 73, which is the price for the Baker Family.
A radio telescope's shape can be approximated with the equation y=0.011x^2. Is the relationship between x and y linear? Is it proportional?
Please help solve with steps:
-3 + u = 1/2
----
5
a number multiplied by 1/2 is -5/12
Answer:
- 5/6 is the answer
Step-by-step explanation:
The number which when multiplied by 1/2 is -5/12 is -5/6
How to multiply?Let
The unknown number = x
So,
x × 1/2 = -5/12
1/2x = -5/12
Divide both sides 1/2
x = -5/12 ÷ 1/2
= -5/12 × 2/1
= -10 / 12
= -5/6
Hence, -5/6 id the number need-
-5/6
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Can someone please help me? Thanks
Answer:
693 sq. m.
Step-by-step explanation:
The figure consists of a triangular prism (Bottom Part) and a Triangular Pyramid (Top Part). We will find the volume of each and add it up to get volume of total figure.
1. Volume of Triangular Prism = Area of Triangular Base * Height
Area of Triangular Base = (1/2)*base*height
Given that the triangle is a right triangle, we find the unknown side by using Pythagorean Theorem, which tells us:
Leg^2 + Another Leg^2 = Hypotenuse^2
8.8^2 + Another Leg^2 = 13.7^2
77.44+ Another Leg^2 = 187.69
Another Leg (unknown side, or the base of the triangle) = Sqrt(187.69-77.44) = 10.5 (this is base of triangle)
So, we have:
Area of Triangular Base = [tex]\frac{1}{2}*10.5*8.8=46.2[/tex]
Thus,
Volume of Triangular Prism = 46.2 * 10(given) = 462 sq.m.
2. Volume of Triangular Pyramid = (1/3) * area of triangular base * height
Here, area of triangular pyramid is 46.2 (already found)
the height of the pyramid is 25 - 10 = 15
SO, we have:
Volume of Triangular Pyramid = [tex]\frac{1}{3}*46.2*15=231[/tex] sq. m.
Now we sum them up and get total volume of the figure:
Total Volume of Figure = 462+ 231 = 693 sq. m.
Divide the following polynomials
(2x2+x+3)/ (x-2)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
2
x
-
3
2
x
2
-
3
x
+
5
Divide the highest order term in the dividend
2
x
2
by the highest order term in divisor
2
x
.
x
2
x
-
3
2
x
2
-
3
x
+
5
Multiply the new quotient term by the divisor.
x
2
x
-
3
2
x
2
-
3
x
+
5
+
2
x
2
-
3
x
The expression needs to be subtracted from the dividend, so change all the signs in
2
x
2
−
3
x
x
2
x
-
3
2
x
2
-
3
x
+
5
-
2
x
2
+
3
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
x
-
3
2
x
2
-
3
x
+
5
-
2
x
2
+
3
x
0
Pull the next term from the original dividend down into the current dividend.
x
2
x
-
3
2
x
2
-
3
x
+
5
-
2
x
2
+
3
x
0
+
5
The final answer is the quotient plus the remainder over the divisor.
x
+
5
2
x
−
3
Granola costs $2.79 for 16.4 ounces. At this rate how much does 25 ounces of granola costs? Round to the nearest cent .
Answer:
$4.25
Step-by-step explanation:
Ratio:
2.79:16.4 = x:25
16.4 × x
2.79 × 25
Cross multiply: 16.4x = 69.75
Then divide: 69.75 ÷ 16.4 = $4.25
What is the measure of the exterior angle ?
70
180
110
Answer:
110
Step-by-step explanation:
A bump is 180 degrees as well as a triangle. So 90+20=110 and 180-110=70. Meaning 180-70 =110
Answer:
110
Step-by-step explanation:
Solve for the angle in the triangle
70+90+ x=180180-110= xx=70solve for the "?"
180=70+?180-70=?110=?Mia is 160.2 centimeters tall.Rosa is 165.1 centimeters tall.how much taller is Rosa the Mia?
Answer:
4.9
Step-by-step explanation:
165.1-160.2
13 lb7 oz + 10 lb2 oz
Final answer:
The sum of the two weights, 13 lb 7 oz and 10 lb 2 oz, is 23 lb 9 oz. You add the ounces first, which don't need conversion, and then add the pounds.
Explanation:
Adding Pounds and Ounces
The question involves adding two weights together that are given in pounds and ounces. To do this, we need to add the ounces together first and then the pounds. The sum of 7 ounces and 2 ounces is 9 ounces. Since there are 16 ounces in one pound, we have no need to convert these ounces to pounds. The sum of 13 pounds and 10 pounds is 23 pounds. Therefore, when we combine these two sums, we arrive at the total weight of 23 pounds and 9 ounces.
Name two points that are reflections of each other across the x-axis.
Answer:
Original point (1,2) and the image is (1,-2).
Step-by-step explanation:
If a point on the coordinate plane reflects across the x-axis then the x-coordinates of the original point and that of the image point will remain the same and the y-coordinates of the original point and that of the image point will only change their signs.
So, a point having coordinates (a,b) when reflected across the x-axis then the point generated after reflection will have coordinates (a,-b).
This is true for any real values of a and b.
So, for example, if (1,2) is a point reflected across the x-axis will generate an image point with coordinates (1,-2). (Answer)
Write the slope-intercept form of the equation of each line.
Answer:y=mx+b
Step-by-step explanation:
At the end of the summer, a store marks down all the outdoor furniture 20%. A family bought 4 chairs that originally cost $102. How much was the cost of the 4 chairs?
Answer:
$81.60
Step-by-step explanation:
A 20% markdown means that the chairs were sold at 80% of the original cost.
Original cost = $102
markdown = 20%
Cost after markdown = original cost* (1-markdown)
Cost after markdown = 102 *(1 - 0.20)
= 102*0.80
= 81.6
Therefore, the 4 chairs were sold at a total cost of $81.60
Choose the point-slope form of the equation below that represents the line that passes through the point (6, −3) and has a slope of fraction 1 over 2 .
Answer:
y + 3 = (1/2)(x -6)
Step-by-step explanation:
When we have the slope m of the line and a point (a,b) which the line passes through, the point-slope form is
y - b = m (x -a)
Since the slope is 1/2 and the line passes through (6, -3), the point-slope equation is
y -(-3) = (1/2)(x -6)
or
y + 3 = (1/2)(x -6)
Estimate. Round to the greatest place value. Circle whether the estimate is greater then or less then the actual product.
Rounding to the greatest place value requires focusing on the digit to the right of the place value you're rounding to. If it's 5 or above, round up, if less, round down. This makes calculations easier by providing an estimated value close to the actual one.
Explanation:In this question, you are asked to estimate a value by rounding to the greatest place value. To do this, you will focus on the digit in the place value you are rounding to and the digit to its right. If the digit is 5 or more, you will round up. If it's less than 5, you will round down. It's called the estimation because it's not an exact value but a value close to the actual one best suited for calculations.
For example, if you have the number 4387 and you want to round it to the greatest place value, which is thousands place, you will look at the hundreds place value which is 8 (greater than 5), so you round up to 5000. Your estimated number, 5000, is greater than the actual product.
The purpose of rounding and estimation is to simplify calculations and analyze systems or data without being bogged down by specificities.
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Use the chart to multiply the binomial by the trinomial.
What is the product?
(y+3)(y2 – 3y+9)
A. y3 + 27
B. 13-27
C. y - 6y? + 27
D. y + 6y2 + 27
Answer:
A) y^3+27
Step-by-step explanation:
(y+3)(y^2-3y+9)
y^3-3y^2+9y+3y^2-9y+27
y^3+27
The product of the polynomial is A = y³ + 27
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
To find the product of (y+3)(y^2 - 3y + 9), we can use the distributive property of multiplication:
(y+3)(y² - 3y + 9) = y(y² - 3y + 9) + 3(y² - 3y + 9)
Now we can simplify each term:
y(y² - 3y + 9) = y³ - 3y² + 9y
3(y² - 3y + 9) = 3y² - 9y + 27
Adding these two simplified polynomial terms, we get:
(y+3)(y² - 3y + 9) = y³ - 3y² + 9y + 3y² - 9y + 27
Simplifying further, we get:
(y+3)(y² - 3y + 9) = y³ + 27
Hence , the product is A = y³ + 27
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What is the answer to the photo
Answer:
96 is the answer maybe of it
A bag of potato chips contain 0.96 grams of sodium. If the bag is split into 8 equal servings, how many grams of sodium will each serving contain
Answer:
0,12 grams
Step-by-step explanation:
0,96:8=0,12
Each serving will contain 0.12 grams of sodium.
Explanation:In order to find out how many grams of sodium each serving contains in the bag of potato chips, we can divide the total amount of sodium in the bag by the number of servings. Given that the bag contains 0.96 grams of sodium and is split into 8 equal servings, we can divide 0.96 by 8 to find the sodium content per serving.
Step 1: Divide 0.96 by 8: 0.96 ÷ 8 = 0.12
Step 2: Each serving will contain 0.12 grams of sodium.
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What's the awnser to x÷9=157
Answer:
x = 1413Step-by-step explanation:
[tex]x\div9=157\\\\\dfrac{x}{9}=157\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}=(9)(157)\\\\x=1413[/tex]
Joan actually likes 30% of her male friends and 20% of her female friends. She has a
total of 200 friends, 45% of them are male. How many female friends does Joan actually like?
Answer:
22
Step-by-step explanation:
The number of male friends : 200 ÷100 × 45 = 90
The number of female friends : 200 - 90 = 110
Joan likes 20% of her female friends and there are total of 110 female friends
20% 110 would be➡ 110 ÷ 100 × 20 = 22
After Megan walked 5 miles her activity tracker have counted 9780 steps David’s activity tracker had counted 11,928 steps after he walked 6 miles.suppose each person step covers about the same distance who takes more steps to walk 1 mile? how many more steps?
Answer:
David took 32 more steps
Step-by-step explanation:
first we need to find out how many steps each person takes every one mile to find that out we divide the steps by how many miles .
megan: 9780÷5= 1956 steps in one mile
David: 11928÷6= 1988 steps in one mile
then you subtract to find by how many more steps .
1988-1956 =32
david took 32 more steps
A stove that cost $500 will be on sale next week for 25% off it’s regular price what is the amount of savings
Final answer:
To calculate the savings of 25% off a $500 stove, you multiply 500 by 0.25 to get a savings of $125.
Explanation:
The question asks us to calculate how much money will be saved on a stove that is on sale for 25% off its regular $500 price. To find the amount of savings, we need to calculate 25% of $500. This is done by multiplying the original price by the percentage discount in decimal form.
The percentage in decimal form is 0.25 (since 25% is 25 per hundred, or 25/100), hence, we multiply 500 by 0.25 to find the savings:
500 × 0.25 = $125.
Therefore, the amount of savings from the original price during the sale is $125.