Answer:
Value of x = 5 .
Step-by-step explanation:
Combined variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others.
Given: x varies directly with y and inversely with z.
i.e [tex]x \propto y[/tex] and [tex]x \propto \frac{1}{z}[/tex]
then we have the combined variation as;
[tex]x = k\frac{y}{z}[/tex] ......[1] where k is the constant variation.
Substitute the value of x =20 when y =8 and z = 4 to solve for k;
[tex]20 = k\frac{8}{4}[/tex]
Simplify:
[tex]20 = 2k[/tex]
Divide both sides by 2 we get;
[tex]k = 10[/tex]
Now, substitute k =10 , y =4 and z = 8 to find x;
Using [1] we have;
[tex]x = 10 \times \frac{4}{8} = 10 \times \frac{1}{2} = 5[/tex]
Therefore, the value of x is, 5
The problem involves the concept of direct and inverse variation. From the given conditions, a constant of variation 'k' is calculated as 1.6. Using this 'k', x is found to be 20 when y is 4 and z is 8.
Explanation:This question involves the concept of direct and inverse variation. When it is stated that 'x varies directly and inversely with z', it implies a relationship which can be written in the form of y = kx/z, where k is a constant of variation.
To find the constant, we plug in the provided values for x, y, and z into our equation. Hence, using the known values (x=20, y=8, and z=4), our equation becomes 8 = 20k/4. Simplifying this gives us k = 1.6.
Now, to find the value of x when y=4 and z=8, we substitute these into the equation giving us 4 = 1.6x/8. Solving for x, we find that x = 20.
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Please help!! Which is correct
Answer:
3rd
Step-by-step explanation:
Just look at the second equation in each system (no need to look at the others). The third is the only one that makes sense. The total value means the number of coins multiplied by value of each. The value in dollars is $9.35
If the value in the equation is in dollars, the variables must be multiplied by values in dollars. You can't multiply with 5 cents per nickle to equal 935 dollars. Makes no sense.
Answer:
C
Step-by-step explanation:
The difference between the dimes and quarters is 3. There are more dimes than quarters.Therefore the equation that expresses that fact is d - q = 3The Answer is C
Irene makes 4 2/3 cups of pancake batter . she splits the
batter into 2 bowls . she mixes blueberries into 2 1/4 cups of batter and walnuts into the rest of the batter
1 . Estimate how much of the batter has walnuts in it .explain your estimate.
2 . find the actual amount of batter that has walnuts in it . explain how you your answer is reasonable .
Answer:
Step-by-step explanation:
An estimate is usually a guess, but I somehow think that's not what you want.
She starts with 4 2/3 cups of batter. When she divides it into two, one of the batters has 2 1/4 cups. That's the one she puts blueberries in.
The other batter is the one you are interested in. How big is it?
Estimate: One
The estimated size would be 4 2/3 - 2 1/3 = 2 1/3 which is an estimate. It is just taking the closest number to use so you don't have to grab your calculator.
Actual Size: Two
4 2/3 - 2 1/4 is the size of the second batter. Since 2/3 is greater than 1/4 you need only subtract the whole numbers and then the fractions.
Whole number subtraction: 4 - 2 = 2
Fraction subtraction: 2/3 - 1/4
Find the Lowest common multiple between 3 and 4: It is 12. 3 and 4 are prime to each other. They have nothing in common.
2/3 to 12s: (2*4)/(3*4) = 8 / 121/4 to 12s: (1 *3) / (4*3) = 3/128/12 - 3/12 = 5/12So the actual size of the batter containing the walnuts is 2 5/12
State whether the fuction is bounded above, bounded below, or bounded. y=32
Hello.
The answer is: Bounded.
This is correct because 32 is the endpoint and the real number of Y.
Have a nice day.
Answer:c. bounded,
Step-by-step explanation: got it correct on edge.
There are 90 fith-grade students going on a feild trip. Each student gives the teacher $9.25 to cover admission to the theater and for lunch. Admission for all the students will cost $315, and each student will get an equal amount to spend on lunch. How much will each fifth grader get to spend on lunch?
Answer:
they each get $5.75 for lunch
Step-by-step explanation:
9.25 x 90 students = 832.50
832.50 -315 = 517.50
517.50 / 90 = 5.75
the product of p and 9
Answer:
The answer is p · 9
Step-by-step explanation:
Product means multiplication
Answer:
The answer is p · 9
but, on gradpoint the answer is 9p
Step-by-step explanation:
50% of one-twentieth of the product of 12 and 5z + 5.
Final answer:
To simplify 50% of one-twentieth of the product of 12 and 5z plus 5, you first calculate the product (60z), take one-twentieth (3z), find 50% of that (1.5z), and then add 5 to get the simplified expression 1.5z + 5.
Explanation:
The question asks to simplify the expression 50% of one-twentieth of the product of 12 and 5z plus 5. Here are the steps to simplify this expression:
Firstly, calculate the product of 12 and 5z, which is 60z.
Then, find one-twentieth of this product, which is 60z / 20 = 3z.
50% of 3z is 1.5z.
Finally, add 5 to 1.5z, which gives you 1.5z + 5 as the simplified expression.
So, the simplified expression is 1.5z + 5.
50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]
To calculate 50% of one-twentieth of the product of [tex]\(12\) and \(5z + 5\)[/tex], we'll follow these steps:
Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\)[/tex].
[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]
Step 2: Calculate one-twentieth of the product.
[tex]\[ \text{One-twentieth of the product} = \frac{\text{Product}}{20} \][/tex]
Step 3: Calculate 50% (or half) of one-twentieth of the product.
[tex]{50% of one-twentieth of the product}[/tex] = [tex]\frac{1}{2} \times \frac{\text{Product}}{20} \][/tex]
Now, let's perform the calculations step by step:
Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\):[/tex]
[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]
[tex]\[ = 12 \times 5z + 12 \times 5 \][/tex]
[tex]\[ = 60z + 60 \][/tex]
Step 2: Calculate one-twentieth of the product:
[tex]\[ \text{One-twentieth of the product} = \frac{60z + 60}{20} \][/tex]
[tex]\[ = \frac{60z}{20} + \frac{60}{20} \][/tex]
[tex]\[ = 3z + 3 \][/tex]
Step 3: Calculate 50% of one-twentieth of the product:
{50% of one-twentieth of the product} =[tex]\frac{1}{2} \times \left(3z + 3\right) \][/tex]
[tex]\[ = \frac{1}{2} \times 3z + \frac{1}{2} \times 3 \][/tex]
[tex]\[ = \frac{3z}{2} + \frac{3}{2} \][/tex]
So, 50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]
Given the numbers x = a and y = –b, which statement is true? A. –|x| = a and –|y| = b B. |–x| = –a and |–y| = b C. |x| = –a and –|y| = –b D. |x| = a and |y| = b
Answer:
D) |x| = a and |y| = b
Step-by-step explanation:
Given the numbers x = a and y = –b
Absolute function always gives the output as a positive number
Absolute function of |-x|= x
For example |5|= 5 and |-5| = 5
Given x=a
|x| = |a| = a, so |x| = a
Given y=-b
|y| = |-b| = b , so |y| = b
Hence, |x| = a and |y| = b
If quadrilateral ABCD is congruent to quadrilateral EFGH, then what corresponding side is congruent to side EF? (5 points)
Answer:
Side AB
Step-by-step explanation:
Draw two congruent quadrilaterals.
Label the sides of one A,B,C,and D.
Label the sides of the other E,F,G,and H
Because the sides match up with the order in which they appear in if they are congruent, The first two letters(E and F) should be equivalent to the first two letters of the other shape(A and B).
find the value of x in the figure below Assume that the lines are parallel
The value of x is 30.
We are given that lines l and m are parallel. We are asked to find the value of x.
Since we are given that l and m are parallel, we can use the property of alternate exterior angles.
This property states that when two lines are cut by a transversal, the alternate exterior angles are congruent.
In the diagram, we see that ∠A and 2x+15 ∘ are alternate exterior angles. Therefore, we have:
∠A=2x+15 ∘
We are also given that ∠A=75 ∘ .
Substituting this value into the equation above, we get:
75 ∘ =2x+15 ∘
Solving for x, we get:
2x=75 −15 ∘
2x=60 ∘
x= 60/2 ∘
x=30∘
Therefore, the value of x is 30 ∘ .
Determine whether the ratios are equivalent 8/7 and 9/7. Need help on #’s 7-12 plz
The ratios 8/7 and 9/7 are not equivalent. Using cross multiplication, we find that the cross products are different, signaling that these two ratios are not equivalent.
Explanation:To determine whether the ratios 8/7 and 9/7 are equivalent, we can cross multiply. In this case, if the two products are equal then the ratios would be equivalent.
Cross multiplication is a method used to test if two ratios are equivalent. It involves multiplying the numerator of the first fraction by the denominator of the second fraction and comparing that product with the product of the denominator of the first fraction and the numerator of the second fraction. If the two products are equal, then the two fractions are equivalent.
Using this method, the cross products of the ratios 8/7 and 9/7 are (8 * 7) and (9 * 7), which are 56 and 63, respectively. Since these two products are not equal, the two ratios are not equivalent.
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What is the sum of 4a^2 − 7a − 5 and −8a^2 − 2a + 7?
5. State whether the number 91 is prime, composite, or neither.
Answer:
91 is a composite number
Step-by-step explanation:
A prime number is the positive number, which has factors 1 and itself.
Example : 1,3,5,7
Clearly 91 is not a prime number, as its factors are:
91 = 1,7,13,91
It has more than 2 factors (1 and itself), hence 91 is a composite number.
Composite number is the number which has factors other than 1 and itself.
Answer:
91 is composite
Step-by-step explanation:
its factors are 1, 7, 13, 91
Please help me with number 6
The answer is C) $250
Answer:
The answer is 250 dollars. to find this do 25 times 1000. the placement is 25 over 100 and x as in the amount were trying find over 1000.
Step-by-step explanation:
If 9 is added to twice a number and this sum is multiplied by 6, the result is the same as if the number is multiplied by 7 and 14 is added to the product. What is the number?
Answer:
The number is -1.
Step-by-step explanation:
Let the number be represented by n.
Then "9 is added to twice a number and this sum is multiplied by 6" is represented by 2n + 9, and
" the number is multiplied by 7 and 14 is added to the product" is
7n + 14.
Then the complete equation is 2n + 9 = 7n + 14.
We must solve this for n. To accomplish this, subtract 2n from both sides, obtaining 9 = 5n + 14. Then subtract 14 from both sides, obtaining
-5 = 5n. Then n must be -1.
Answer:
The number is -8
Step-by-step explanation:
Developing an equation
Read these phrases a little a time.
9 is added to twice a number = 2x + 9This sum is multiplied by 6 = 6* sum = 6 * (2x + 9) Note the brackets.is the same thing as means = the number multiplied by 7 = 7xand 14 is added to the product 7x + 14So what you have is equation: 6*(2x + 9) = 7x + 14Solution
6*(2x + 9) = 7x + 14 Remove the brackets on the left12x + 54 = 7x + 14 Subtract 14 from both sides12x + 54 - 14 = 7x + 14 - 14 Collect terms12x + 40 = 7x Subtract 12x from both sides.12x - 12x + 40 = 7x - 12x Combine40 = -5x Divide by - 540/-5 = x Do the division- 8 = xWhen solving for x what would (8x-46) + (10x-8)
Answer:
18x - 54 :) :( :) :)Please help! I have 5 more mins on my timed quiz. I WILL GIVE BRAINLIEST!
1. Multiply.
3√⋅22√⋅58√⋅18−−√
Enter your answer, in simplest radical form, in the box.
2. Use the properties of exponents to simplify the expression all the way.
(2x4y−3)−1
2x4y3
2y3x4
2x4y3
y32x4
3. Use properties of exponents to simplify the following expression.
2x4y−4z−33x2y−3z4
2x23yz7
2yz3x2
2x4y3z
3x2y3z42
only know number 1 sorryyyy
1 . 11^2⋅√58
Answer:
1. [tex]18 \cdot \sqrt{638}[/tex]
2. [tex]\frac{y^{3}}{2 x^4}[/tex]
3. [tex]\frac{2 x^2}{3 y z^{−7}} [/tex]
Step-by-step explanation:
1. Assuming the expression is:
[tex]3 \cdot \sqrt{22} \cdot \sqrt{58} \cdot \sqrt{18}[/tex]
Express the radicands as multiplication of prime numbers:
[tex]3 \cdot \sqrt{11 \cdot 2} \cdot \sqrt{2 \cdot 29} \cdot \sqrt{3^2 \cdot 2}[/tex]
Distribute the radicals over the multiplication where a power is present:
[tex]3 \cdot \sqrt{11 \cdot 2} \cdot \sqrt{2 \cdot 29} \cdot \sqrt{3^2} \cdot \sqrt{2}[/tex]
[tex]3 \cdot \sqrt{11 \cdot 2} \cdot \sqrt{2 \cdot 29} \cdot 3 \cdot \sqrt{2}[/tex]
[tex]9 \cdot \sqrt{11 \cdot 2} \cdot \sqrt{2 \cdot 29} \cdot \sqrt{2}[/tex]
Apply the inverse of distributive property of radicals over multiplication:
[tex]9 \cdot \sqrt{11 \cdot 2 \cdot 2 \cdot 29\cdot 2}[/tex]
[tex]9 \cdot \sqrt{11 \cdot 2^2 \cdot 29\cdot 2}[/tex]
[tex]9 \cdot \sqrt{11 \cdot 29\cdot 2} \cdot \sqrt{2^2} [/tex]
[tex]9 \cdot \sqrt{638} \cdot 2 [/tex]
[tex]18 \cdot \sqrt{638}[/tex]
2. Assuming the expression is:
[tex](2 x^4 y^{-3})^{-1}[/tex]
Distribute the exponent over the multiplication
[tex]2^{-1} \cdot {(x^4)}^{-1} \cdot {(y^{-3})}^{-1}[/tex]
[tex]\frac{1}{2} \cdot x^{-4} \cdot y^{3}[/tex]
[tex]\frac{1}{2} \cdot \frac{1}{x^4} \cdot y^{3}[/tex]
[tex]\frac{y^{3}}{2 x^4}[/tex]
3. Assuming the expression is:
[tex]\frac{2 x^4y^{-4}z^{-3}}{3 x^2 y^{-3} z^4}[/tex]
Group by similar terms and simplify:
[tex]\frac{2}{3} \cdot \frac{x^4}{x^2} \cdot \frac{y^{-4}}{y^{-3}} \cdot \frac{z^{-3}}{z^4}[/tex]
[tex]\frac{2}{3} \cdot x^2 \cdot y^{-1} \cdot z^{-7}[/tex]
[tex]\frac{2 x^2}{3 y z^{-7}} [/tex]
D-I are the measurements of the lengths of the sides of triangles. Identify the types of
triangles
d. 45 cm 61 cm 60 cm e. 30 cm, 31cm, 30 cm f. 4 cm, 5ft, 4 cm
g. 89mm, 89mm, 89mm h. 9 in, 5in, 3 in i. 22cm, 22cm, 22in
J-O are the measurements of the angles of triangles. Identify the type of triangle.
j. 900, 350, 550 k. 600, 600, 600 l. 700, 550, 550
m. 350, 400, 1000 n. 460, 460, 440 o. 1200, 300, 300,
Answer:
The sum of the interior angles of a triangle is 180 degrees.
d. Scalene
e. Isosceles
f. Isosceles
g. Equilateral
h. Scalene
i. Equilateral
j. Right
l. Acute
m. Obtuse - doesn't add to 180 not a triangle
n. Acute - doesn't add to 180 not a triangle
o. Obtuse
Step-by-step explanation:
The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.
Side lengths: Compare the side lengths and see if any are equal to determine the type.
Scalene: 3 different lengthsIsosceles: 2 equal lengths and 1 differentEquilateral : 3 equal sidesAngle Measures: Compare the angles measures to 90 degrees.
Right: If one angle is equal to 90Acute: All angles are less than 90 degreesObtuse: One angle is greater than 90 degreesThe set of ordered pairs below represents a linear function. Find the rate of change. {(1,4), (2,6), (3,8), (4,10)} The rate of change (slope) =
Answer: 2/1 is the rate of change.
Step-by-step explanation: 1/4 and 2/6. Take these 2 numbers. 2-1=1 and 6-4=2. Therefore we get 2/1.
Amelia and Brianna work at a furniture store. Amelia is paid $240 per week plus 6% of her total sales in dollars, xx, which can be represented by g(x)=240+0.06xg(x)=240+0.06x. Brianna is paid $130 per week plus 8.5% of her total sales in dollars, xx, which can be represented by f(x)=130+0.085xf(x)=130+0.085x. Determine the value of xx, in dollars, that will make their weekly pay the same.
Answer:
x = $4400
Step-by-step explanation:
If we want their pay to be the same, the equations have to be equal
g(x)=240+0.06x = f(x)=130+0.085x
240 + .06x = 130+0.085x
Subtract .06x from each side.
240 + .06x - .06x = 130+0.085x-.06x
240 = 130 +.025x
Subtract 130 from each side
240-130 = 130-130 +.025x
110 = .025x
Divide each side by .025 to isolate x
110/.025 = .025x/.025
4400 =x
How do you solve for a²+b²=289 when b+a=23
Answer:
1 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
{a}^{2}+bb=289a
2
+bb=289
2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
{a}^{2}+{b}^{2}=289a
2
+b
2
=289
3 Subtract {b}^{2}b
2
from both sides
{a}^{2}=289-{b}^{2}a
2
=289−b
2
4 Take the square root of both sides
a=\pm \sqrt{289-{b}^{2}}a=±√
289−b
2
5 Rewrite 289-{b}^{2}289−b
2
in the form {a}^{2}-{b}^{2}a
2
−b
2
, where a=17a=17 and b=bb=b
a=\pm \sqrt{{17}^{2}-{b}^{2}}a=±√
17
2
−b
2
6 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
a=\pm \sqrt{(17+b)(17-b)}a=±√
(17+b)(17−b)
Will give brainliest please help ASAP
Answer:
D
Step-by-step explanation:
y>-3x+1 Negative slope
y<x+2 Positive slope
< or > have dotted line
< or > have a solid line
> or > means solutions are above the line
< or < means solutions are below the line
The one with negative slope has a dotted line and solutions above it.
The one with positive slope has a solid line and solutions below it.
your network wants you. to cut your expenses per episode. they have given you a budget of $85,134 for the next 6 episode. how much do you have to spend per episode?
At the beginning of the week Fayez writes down the mileage of his limo at 2529 at the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during this week. The handbook states the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limo uses 1 gallon of petrol for every 20 miles that week. 1 gallon = 4.54 litres . Did his limo use 1 gallon of petrol every 20miles that week. Show your answer clearly
Answer:
No. It used 1 gallon in 18.41 miles.
Step-by-step explanation:
He travelled 2834 - 2529 = 305 miles.
So his consumption is 305 / 75.2 = 4.056 miles/litre.
This equals 4.056*4.54 = 18.41 miles / gallon.
So this is less than the 1 gallon every 20 miles stated by the handbook.
Answer: His limo used 1 gallon fuel for 18.4136 miles.
Step-by-step explanation:
Fayez covered distance:
2834 - 2529 = 305 miles.
He used fuel = 75.2 litres
75.2/4.54 = 16.5638 gallons petrol used.
His limo covered distance / total petrol used = 305 miles / 16.5638 gallons petrol = 18.4136 miles per gallon.
That is less than 20 miles per gallon
jordan is chopping wood for the winter. for 10 days on a row he follows the same process: in the morning he chops 20 pieces of wood and in the evening he chops an additional 30 pieces of wood on the 11th day jordan chops only 5 pices of wood write a numerical expression with parentheses for the total number of pieces of wood jordan chopped. (do not simplify your expression)
What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)
Answer:
remainder = 290
Step-by-step explanation:
[tex]\frac{3x^3-4x^2+2x+8}{x-5}[/tex]
= 3x² + 11x + 57 + [tex]\frac{290}{x-5}[/tex]
quotient = 3x² + 11x + 57 and remainder = 290
explain whether a quadratic function can have both a maximum value and a minimum value
A quadratic function can not have a maximum and minimum value. It can only take on one of those. The quadratic only makes one turn, so if the quadratic opens upwards, there is a minimum. If the quadratic opens downwards, there is a maximum.
A quadratic function can have either a maximum value or a minimum value, but not both.
Explanation:A quadratic function can have either a maximum value or a minimum value, but not both. Whether it has a maximum or minimum value depends on the coefficient of the quadratic term (a) in the function. If a is positive, the graph of the quadratic function opens upwards and has a minimum value. If a is negative, the graph opens downwards and has a maximum value.
For example, the function y = x² has a minimum value of 0 at the vertex of the parabola, while the function y = -x^2 has a maximum value of 0 at the vertex.
Therefore, a quadratic function cannot have both a maximum value and a minimum value.
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What is the quotient of
y-5\sqrt{2y^2-7y-15}
A. 2y + 3
B. 2y − 3
C. 2y − 17y R −70
D. 2y − 17y R 70
Answer:
None of these
Step-by-step explanation:
y-5\√(2y2 - 7y -15)
On simplifying 2y2 - 7y -15, we get
2y2 – (10-3)y -15
= 2y2 – 10y -3y-15
= 2y(y-5)-3(y-5)
= (2y-3)(y-5)
On squaring nominator and denominator we get
(y-5)2/(2y-3)(y-5)
= (y-5)/(2y-3)
So the quotient becomes, 5/2
While the remainder becomes 2.5
Answer:
I think its A
Step-by-step explanation:
a fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put information into a system of linear equations.
Answer:
X = apple
y = orange
4x + 4y = 10
6x + 6y = 12
Step-by-step explanation:
Answer:
4a+4r = 10
6a + 6r = 12
No solutions
Step-by-step explanation:
a = cost of the apple
r = cost of the orange
4a+4r = 10
6a + 6r = 12
Divide the first equation by 2 and the second equation by 6
2a+2r = 5
a +r = 2
Multiply the second equation by -2 so we can eliminate a
-2a -2r = -4
Add the first equation
2a+2r = 5
-2a -2r = -4
---------------------
0 = 1
This system is inconsistent and has no solutions
You work for a landscaper that has a customer needing to seed an area of land 80 feet by 40 feet in size. The garden center has 5-pound bags of grass seed. Each bag of seed can cover 25 square yards of land. You calculate that the area you need to seed is 3200 square feet. You divide by 25 to find that you need 128 bags to seed the area. Is this correct?
Answer:
No, the solution discussed in question is not correct.
Step-by-step explanation:
Length of the garden ,l= 80 feet
Breadth of the garden ,b= 40 feet
Area of the rectangle = l × b
Area of the garden = A
[tex]A=l\times b = 80 ft\times 40 ft = 3,200 ft^2[/tex]
Area covered by 1 bag of seeds of grass = [tex]25 yard^2=225 ft^2[/tex]
[tex]1 yard^2 = 9 ft^2[/tex]
Bags of seed of grass covering area of [tex]3,200 ft^2[/tex]:
[tex]\frac{3200 ft^2}{225 ft^2}=14.22[/tex]
14.22 bags of seed of grass will occupy the area covered by the garden.
I don’t understand all 3 of them