[tex]8x+5y=-17[/tex] when y is -5
Substitute for y with given value:
[tex]8x+5(-5)=-17[/tex]
[tex]8x-25=-17[/tex]
Add 25 to both sides:
[tex]8x-25+25=-17+25[/tex]
[tex]8x=8[/tex]
Divide both sides by 8:
[tex]\dfrac{8x}{8} =\dfrac{8}{8}[/tex]
[tex]\fbox{x = 1}[/tex]
Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.
Answer:
A. 2w² + 8w
Step-by-step explanation:
rectangle: A = w(w+4) = w² + 4w
triangle: A = 1/2(2(w+4)(w)) = 1/2(2w+8)(w) = 1/2(2w²+8w) = w² + 4w
Total Area = w² + 4w + w² + 4w = 2w² + 8w
Audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (–1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)
The reasonable solutions for this situation is (1, 3.5) and (2, 2)
What is Graph?A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.
Audrey has x pounds of red grapes and y pounds of green grapes.
She has less than 5 pounds of grapes in all, hence:
x + y < 5
Also, x ≥ 0, y ≥ 0
a) The option (–1, 2) is wrong because x = -1 < 0
b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5
c) The option (2, 2) is correct because 2 + 2 = 4 < 5
d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.
e) The option (5, 0) is wrong because 5 + 0 is not less than 5
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Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Answer:
yes, the board is long enough
Step-by-step explanation:
5.5 in x 4 walls = 22 inches
The board is 24.5 in, so there is enough.
24.5 > 22, there is an extra 2.5 in left over.
Matthew scored a total of 168 points in his basketball season. He scored 147 of those points in the regular season and the rest were scored in his playoff game. What percent of his total points did he score in the playoff game?
Answer:
168 - 147 = 21
21/168 = 12.5
b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
Cost (in dollars)
2
10
3
9
15 45
The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $50:
Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.
The best way to find out how many people will go to movie with $50 is by looking at the table.
So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,
Step-by-step explanation:
the graph shows the total weight of abox of cereal, y, as a function of the amount of cereal in the box, x. what is the weight of the box when it is empty?
Answer:
3
Step-by-step explanation:
Solve the answer please
Answer:
A
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
140° is an exterior angle of the triangle , then
∠ B + 90° = 140° ( subtract 90° from both sides )
∠ B = 50°
∠ ACB and ∠ DCB are a linear pair and sum to 180° , that is
∠ ACB + 140° = 180° ( subtract 140° from both sides )
∠ ACB = 40°
What are the 4 steps to solve by elimination?
Elimination is a very easy method when it comes to solving simultaneous equations.
First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.
The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given
Now take one of the equations and multiply it by -1.
Add the equations up to eliminate the variable and derive the other variable(s)
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The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
0/1
Write the ratio of ponies and goats to rabbits and
sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answer:
3/7
Step-by-step explanation:
3 ponies + 3 goats = 6 total
8 rabbit + 6 sheep = 14 total
6/14 simplified is 3/7.
Central Park in New York City is rectangular with a length of 2.5 miles and a width of 0.5 mile. During an afternoon, its population density is about 15 people per acre. Find the number of people in the park that afternoon. One acre is equal to 1640 square mile.
On solving the provided question, we can say that Surface Area of central park = 2.5 × 0.5 = 1.25 square mile
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Surface Area of central park = 2.5 × 0.5 = 1.25 square mile
1 acre = 1/640 square mile
1.25 square mile = 1.25 ÷ 1/640 = 800 acre
Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people
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What is the mole of H2?
One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
What is mole?A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.
What is Avogadro's number?Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.
One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.
The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
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Please solve area of figure
Formula and radius of figure in the picture
Area of circle and formula and radius of circle is 9 pi ( x y ^3 )^3.
How can you calculate area using pi and radius?A circle's area is equal to pi times the radius squared (A = r2).
Pi times the radius r squared equals the area of a circle.
π ⋅ ( r a d i u s)2
In the formula for the area of a circle, substitute the value of the radius r =3. 3.14 is about how big a number pi is.
pi * 3^2
Raise 3 to the power of 2 to arrive at 9.
pi * 9
9 must be moved to the left of. 9 pi ( x y ^3 )^3.
Area of circle and formula and radius of circle is 9 pi ( x y ^3 )^3.
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96 - y = 161 solve for y
Answer: -65
Step-by-step explanation:
96 - y = 161
-y = 161 - 96
-y = 65
y = -65
Amy operates a coffee kiosk and is blending her special house coffee. She is mixing Kenya beans that cost $9. 00 per pound with Colombia
beans that cost $7. 50 per pound to create a 30 pound blend that sells for $8. 50 per pound. How many pounds of Kenya beans and how many
pounds of Colombia beans does Amy need to use to create her blend?
So Amy needs to use 2 pounds of Colombia beans and 32 pounds of Kenya beans to create her blend.
Define Unitary Method.The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What is direct and indirect variation in the unitary method?We are aware that an inverse variation or indirect variation occurs when two values are coupled in a way that a rise in one generates a corresponding reduction in the other, and vice versa.
Let x be the number of pounds of Kenya beans and y be the number of pounds of Colombia beans. We know that:
x + y = 30 (since the blend is 30 pounds)
We also know that the blend sells for $8.50 per pound, so the total cost of the blend is:
8.50(x + y) = 8.50(30) = $255
We know that the cost of the Kenya beans is $9.00 per pound and the cost of the Colombia beans is $7.50 per pound, so the total cost of the Kenya beans is:
9.00x and the total cost of the Colombia beans is 7.50y
We can set up the following equation:
9x + 7.5y = 255
We have 2 equations and 2 variables, we can solve this system of equation by different methods, one of them is substitution:
x + y = 30
9x + 7.5y = 255
We can substitute the first equation into the second equation
9(x + y) + 7.5y = 255
9(30) + 7.5y = 255
270 + 7.5y = 255
7.5y = -15
y = -2
So Amy needs to use 2 pounds of Colombia beans. We can substitute that value into the first equation to find the amount of Kenya beans:
x + (-2) = 30
x = 32
So Amy needs to use 32 pounds of Kenya beans.
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Nolan is a waiter at a restaurant. Each day he works, Nolan will make a guaranteed wage of $25, however, the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on. How much would Nolan expect to earn in a day on which he waits on 12 tables? How much would Nolan expect to make in a day when waiting on tt tables?
Nolan would expect to earn $157 in a day when he waits in 12 tables.
Now, According to the question:
We have the following information:
Each day Nolan works, Nolan will make a guaranteed wage of $25, however the additional amount that Nolan earns from tips depends on the number of tables he waits on that day. From past experience, Nolan noticed that he will get about $11 in tips for each table he waits on.
Now, for waiting on 12 tables, he will get the fixed amount of 25 dollars and the amount for 12 tables.
So, the total amount will be:
25+11 × 12
$157
Hence, Nolan would expect to earn $157 in a day when he waits in 12 tables.
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What is the third side of a triangle calculator?
The third side of a triangle can be calculated using the Pythagorean Theorem.
This theorem states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite the right angle.
Formula:
[tex]a^2 + b^2 = c^2[/tex]
Determine the two side lengths of the triangle
Calculate the sum of the squares of the two side lengths.
Calculate the square root of the sum of the squares of the two side lengths. This is the length of the third side (the hypotenuse).
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Choose two statements that are true for this expression.
6x3 -8x^2- 40/y+21
Observing the given equation, The answer is The degree of polynomial is 3 and the equation has variables 'x' and 'y'.
What do you mean by equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equals sign (=), for example, 2 + 2 = 4. Equations can be used to express relationships between different quantities and can be used to solve problems in many areas of mathematics and science. Equations can also be represented graphically, and they can be manipulated or transformed to make solving them easier.
What is degree of polynomials?A polynomial is a mathematical expression that is made up of a sum of powers in one or more variables. The degree of a polynomial is the highest power of the variable(s) present in the polynomial. For example, in the polynomial expression 3x^2 + 2x - 5, the highest power of x is 2, so the degree of the polynomial is 2. A degree 0 polynomial is a constant polynomial, which is just a number. The degree 1 polynomial is a linear equation, and degree 2 polynomial is a quadratic equation. In general, the degree of a polynomial can give an idea about the behavior of the polynomial function. As the degree of a polynomial increase, the shape of the function become more complex.
[tex]6x^3 - 8x^2 -\frac {40}{y} +21[/tex]
The degree of polynomial is 3.
The equation has variable 'x' and 'y' .
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45. Sliding Down a Hill
Ojemba is sitting on a sled on the side of
a hill inclined at 60°. The combined weight of Ojemba and the
sled is 160 pounds. What is the magnitude of the force required
for Mandisa to keep the sled from sliding down the hill?
If Ojemba is sitting on a sled on the side of a hill inclined at 60° and weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N .
the inclination angle of the the side of the hill is = 60° ;
the compound mass of Ojemba and Sled is = 160 pounds ,
On conversion we get the mass in Kg is = 72.57 Kg .
the acceleration due to gravity is , [tex]g = 9.8 m/s^{2}[/tex] ;
The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;
[tex]F = mgSin\theta[/tex] , Substituting the values ,
we get ;
[tex]F = 72.57\times 9.8\times Sin(30\textdegree)[/tex]
[tex]F = 72.57\times 9.8\times \frac{1}{2}[/tex] ;
So , [tex]F = 355.59 N[/tex] .
The required magnitude of the force is 355.59 N .
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a ski area claims that its lifts can move 47000 people per hour. if the average lift carries people about 200m (vertically) higher, estimate the maximum total power needed?
The peak is located at R=1 according to a power curve analysis. To put it another way, the load and source resistance must match.
At what point does maximum total power occur?The ski area's name needs to be changed first. Squaw is not a kind way to refer to a woman. It is an expression that refers to female genitalia. (a decent slang equivalent in English begins with "c" and rhymes with "runt") During my time as a teacher in an Indian school, I learned this in a very embarrassing manner.
If we suppose that each person weighs roughly 70 kilograms (154 lbs) on Earth, then the power required to simply raise the people is P = W/t, and since W = mgh in this situation, P = W/t = mgh/t = (47,000 people)(70 kg/person).
(2 MW) = (1791222.222 W)(9.8 N/kg)(200 m)/(3600 s).
The complete question is:
Squaw Valley ski area in California claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.
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Please help I have a learning disability and need help with this.
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
( 3 6) 9 and 3 (6 9)
yes, it uses the Associative Property
yes, it uses the Commutative Property
yes, it uses the Identity Property
no they are not equivalent
Answer:
No, they are not equivalent.
Step-by-step explanation:
The first expression, (3 6) 9, is equal to 9, while the second expression, 3 (6 9), is equal to 3. The two expressions are not equivalent because they do not produce the same result when the operations are carried out. The properties of associativity, commutativity, and identity do not apply to these expressions.
Answer:
no they are not equivalent
Step-by-step explanation:
The two expressions are not equivalent. This is because the distributive property does not apply in this case, as the parentheses on the left side of the expression have precedence over the parentheses on the right side. Therefore, the expression on the left side would be evaluated first, resulting in a different answer than the expression on the right side.
300 grams of type a raisin bran is mixed with 500 grams of type b raisin brad to produce a mixture which is 11% raisins. Type A raisin bran has twice as many raisins per kilogram as type b. What percentage of raisins are each type of raisin bran?
The blend contains 16% of type A and 8% of type B.
What is meant by percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Let p be the percentage of type b used for the mix
2p be the percentage of type a used for the mix
2p × 300 + p × 500 = 0.11 × 800
simplifying the above equation, we get
p = 0.08 or 8%
Substitute the values in the above equation
2p = 2 × 0.08 = 0.16 or 16%
16 % of type a and 8 % of type b exists utilized for the mix.
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The required percentage of raisins are each type of raisin bran are 16% and 8%.
What is meant by percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Let p be the percentage of type b used for the mix
2p be the percentage of type a used for the mix
2p × 300 + p × 500 = 0.11 × 800
simplifying the above equation, we get
p = 0.08 or 8%
Substitute the values in the above equation
2p = 2 × 0.08 = 0.16 or 16%
16 % of type a and 8 % of type b exists utilized for the mix.
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find the value of 15/4 divided 5/8.show you reasong
[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]
In order to divide two fractions, you will need to use the KCF method.
Keep
Change
Flip
This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
Multiply:
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
[tex]\dfrac{15\times8}{4\times5}[/tex]
[tex]=\dfrac{120}{20}[/tex]
Simplify:
[tex]120\div20[/tex]
[tex]=\fbox{6}[/tex]
Answer: 6
Step-by-step explanation:
1. 15/4 divided by 5/8 = 120/20
15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20
2. 120/6 = 6
Simplifying algebraic expression
Answer:
42
Step-by-step explanation:
2 + 3(5) + 5(5)
2 + 15 + 25
Which equals..
42
Answer:
42
Step-by-step explanation:
IF b=5
Now,
2+3b+5b
=. 2 + 3*5 + 5*5
=. 2 + 15 + 25
=. 42
What is the equation of the parabola opening upward with a focus at (9,27) and a directrix of y =11
A. F(x) = 1/16(x-9)^2 + 19
B. F(x) = 1/16(x+9)^2 -19
C. F(x) = 1/32(x+9)^2 -19
D. F(x) = 1/32(x-9)^2 + 19
The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.
What is the equation of the parabola?
The equation can be written as
f(x) = 1/(4p)(x -h)^2 +(k-p)
where (h, k) is the focus, and p is half the distance between focus and directrix.
Here, We have the upward parabola;
Focus at (9,27)
P/2 = 27-19 = 8 Nature of focus
P = 16
so (x-9)^2 = 2py = 32y
y = 1/32(x-9)^2 + 19
The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.
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What is 2(−2x+1)−5x+2= -23
Answer:
Step-by-step explanation:
To solve this equation, you will need to manipulate the equation in order to isolate the variable x on one side of the equation. Here is one way you could solve this equation:
Begin by distributing the 2 on the left side of the equation: 2(-2x+1) = -46 + 2x.
Next, distribute the -5 on the right side of the equation: 2(-2x+1) = -23 - 5x.
Combine like terms on the right side of the equation: 2(-2x+1) = -5x - 23.
Combine like terms on the left side of the equation: -4x + 2 = -5x - 23.
Add 4x to both sides of the equation to isolate the variable on one side: 2 = -x - 23.
Add 23 to both sides of the equation: 25 = -x.
Finally, divide both sides of the equation by -1 to solve for x: x = -25.
Therefore, the solution to the equation is x = -25.
Answer:
x=3
Step-by-step explanation:
2(−2x+1)−5x+2= -23
Distribute
-4x+2-5x+2=-23
Combine like terms
-9x+4=-23
Subtract both sides by 4
-9x=-27
Divide both sides by -9
x=3
Hope this helps :)
how many integer between 20 and 40 divisable by 3
Answer:
4 prime numbers all divisible by 3
Step-by-step explanation:
there are 4 prime numbers between 20 and 40 23, 29, 31, 37 all divisible by 3
Answer:
7 integers
Step-by-step explanation:
We can find how many integers between 20 and 40 are divisible by 3 by looking at the multiples of 3 that lie between 20 and 40.
1: 3 * 7 = 21
2: 3 * 8 =24
3: 3 * 9 = 27
4: 3 * 10 = 30
5: 3 * 11 = 33
6: 3 * 12 = 36
7: 3 * 13 = 39
HELP THIS IS MY LAST PROBLEM
The percentage markup the store made before selling those speakers
are 136.33%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A store bought a set of speakers for $82.86 and sold them for
$195.82.
So, The amount of profit is $(195.82 - 82.86).
= $112.96.
Now, The markup percentage can be obtained by the concept of the percentage change.
Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,
= (112.96/82.86)×100%.
= 136.33%.
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The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than
27 kg
b) Work out the maximum number of dogs that could have a mass of more than
27 kg
a) The minimum number of dogs that could have a mass of more than 27 kg is 6.
b) The maximum number of dogs that could have a mass of more than 27 kg is 18.
We have a table which shows information about the masses of some dogs.
Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.
But we wants minimum of 12 and 6 is 6 .
so, the minimum number of dogs with mass more than 27 kg is 6.
b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.
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Complete question:
The above table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 27 kg
b) Work out the maximum number of dogs that could have a mass of more than 27 kg
find the area of the rectangle whose length is 16cm and breath is 8cm
Answer:
128cm²
Step-by-step explanation:
Formula to find area of rectangle is l×b
In order to find the area of the rectangle we need to apply that formula
[tex]A =lb[/tex]
[tex]A = 16[/tex]×[tex]8[/tex]
[tex]A = 128[/tex][tex]cm[/tex]²
Hence , the area of the given rectangle is 128cm²
How much money should be put into a savings account now that earns 6.0% a year compounded weekly if you want to have 70000 in 15 years?
If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.
How does compound interest work?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.
Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.
A = P(1 +r/n)^(nt)
where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, we have ...
70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)
P = 70000/2.4583 = 28474.96
You would need to deposit 28474.96 in order to have 70000 in 15 years.
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