The 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.
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
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
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:
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 degreesexplain 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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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]
In the diagram below which distance represents the distance from point d to ab
Answer:CD
Step-by-step explanation:
There is a line from A-B and the fastest way to get there is to go "down" c
Answer: The answer is (A) CD.
Step-by-step explanation: We are given to choose the correct option that represents the distance from point D to AB.
We know that the distance between a point and a line is the length of the perpendicular drawn from the point to the line.
So, here CD will be the required distance from point D to AB, because CD is perpendicular from point D to AB.
Thus, (A) is the correct option.
how do you solve problem 33
Answer:
G(-1, 3)
Step-by-step explanation:
You need to try each point in the given equation to see which one does not work.
The definition of the function is that it has two different expressions. The upper expression is used for values of x that are less than or equal to -1.
For values of x less than or equal to -1, the expression is f(x) = 2x + 3.
Look at point F. Its x-coordinate is -1.5. Since -1.5 is less than or equal to -1, use the upper expression. Plug in -1.5 for x and find f(-1.5).
f(x) = 2x + 3
f(-1.5) = 2(-1.5) + 3 = -3 + 3 = 0
That gives point (-1.5, 0), so point F is on the graph of f(x).
Now let's look at point G(-1, 3). For point G, x is -1. Since -1 is also less than or equal to -1, you still use the upper expression for x = -1.
f(x) = 2x + 3
f(-1) = 2(-1) + 3 = -2 + 3 = 1
The point that contains x-coordinate -1 is point (-1, 1). Point G is (-1, 3), so point G is not on the graph of function f.
You already know the answer is point G, but let's continue to show how the other two points are part of the graph of the function.
Point H is (0, 4). For this point, the x-coordinate is 0. The lower expression is used for x greater than -1, and 0 is greater than -1, so you must use the second expression. Now we evaluate the function at x = 0 using the second expression.
f(x) = 4 + x
f(0) = 4 + 0 = 4
giving us point (0, 4).
Point H is (0, 4), so point H is on the graph of the function.
Now we do point J(4, 8). Like for point H, the x-coordinate of point H is greater than -1, so you use the second expression.
f(x) = 4 + x
f(4) = 4 + 4 = 8
giving point (4, 8).
Point J is (4, 8), so it is on the graph.
The only point not on the graph is point G.
Answer: G(-1, 3)
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:
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:
How can I find the factor of
[tex]243 {w}^{4} z - 48z[/tex]
Answer:
3z(3w - 2)(3w + 2)(9w² + 4)
Step-by-step explanation:
take out a common factor 3z from both terms
= 3z(81[tex]w^{4}[/tex] - 16)
81[tex]w^{4}[/tex] - 16 ← is a difference of squares
• a² - b² = (a - b)(a + b)
81[tex]w^{4}[/tex] = (9w²)² → a = 9w² and 16 = 4² → b = 4
= 3z(9w² - 4)(9w² + 4)
9w² - 4 ← is also a difference of squares with a = 3w and b = 2
= 3z(3w - 2)(3w + 2)(9[tex]w^{4}[/tex] + 4)
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
I’m I right?????????????
Answer:
Change "3" to "4"Change "46" to "128"Step-by-step explanation:
The table tells you that for every 1 package, you have 16 tortillas. Thus, the function is y = 16x.
y = amount of tortillas and x = number of packages
To find the number of packages for 64 tortillas, divide 64 by 16-- which gives you 4. Instead of "3" packages, change that number to "4".
To find the amount of tortillas in 8 packages, multiply 8 by 16-- which gives you 128 tortillas. Instead of "46", replace that amount with 128.
Divide 144 tortillas by 16, which gives you 9. The answer you gave is correct.
Multiply 10 packages by 16, which gives you 160-- your answer is also correct here.
In a flower garden, there are 6 tulips for every 9 daisies. If there are 30 tulips, how many daisies are there?
A.
51
B.
43
C.
45
D.
47
Answer: C. 45
Step-by-step explanation:
1. You know that there are 6 tulips for every 9 daisies. Then, if there are 30 tulips, you can write the following expresion, where [tex]x[/tex] is the number of daisies when there are 30 tulips:
[tex]\frac{6}{9}=\frac{30}{x}[/tex]
2. Then, you must solve for x as following:
[tex]6x=30*9\\6x=270\\x=\frac{270}{6}\\x=45[/tex]
3. Therefore, the answer is 45 daisies.
By creating and solving a ratio based on the given relationship of 6 tulips to 9 daisies, it is determined that if there are 30 tulips, there must be 45 daisies in the flower garden. Thus, the correct choice to the student's question is option C) 45 daisies.
To solve this problem, we can set up a ratio based on the information given: there are 6 tulips for every 9 daisies. The ratio of tulips to daisies is therefore 6:9. If there are 30 tulips, this ratio must be multiplied by a certain factor to reach 30. To find this factor, we divide 30 (the actual number of tulips) by 6 (the number of tulips in the ratio), giving us a factor of 5. We then multiply the daisy part of the ratio (9) by 5 to find the actual number of daisies.
6 tulips : 9 daisies = 30 tulips : x daisies
30 / 6 = 5
9 daisies * 5 = 45 daisies
Therefore, if there are 30 tulips in the garden, there are 45 daisies, which corresponds to choice C.
find all the zeros of 2x4+x3-14x2-19x-6 two of its zeros are -2 and -1
Answer:
[tex]-2,\ -1,\ -\dfrac{1}{2},\ 3.[/tex]
Step-by-step explanation:
Consider polynomial [tex]2x^4+x^3-14x^2-19x-6.[/tex]
If x=-2 is its zero, then you can divide the polynomial [tex]2x^4+x^3-14x^2-19x-6[/tex] by [tex]x+2[/tex] and get
[tex]2x^4+x^3-14x^2-19x-6=(x+2)(2x^3-3x^2-8x-3).[/tex]
If x=-1, then the polynomial [tex]2x^4+x^3-14x^2-19x-6[/tex] can be rewritten as
[tex]2x^4+x^3-14x^2-19x-6=(x+2)(x+1)(2x^2-5x-3).[/tex]
The quadratic polynomial has roots
[tex]x_{1,2}=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\cdot2\cdot(-3)}}{2\cdot 2}=\dfrac{5\pm \sqrt{25+24}}{4}=\dfrac{5\pm \sqrt{49}}{4}=3,-\dfrac{1}{2}.[/tex]
Then the polynomial [tex]2x^4+x^3-14x^2-19x-6[/tex] has zeros [tex]-2,\ -1,\ -\dfrac{1}{2},\ 3.[/tex]
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 ∘ .
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.
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).
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.
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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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 = xWill 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.
Which set of points contains the solutions to the inequality y ≤ 8x – 3? A. {(–3,–17), (4,11), (7,19)} B. {(3,22), (2,3), (8,27)} C. {(4,29), (–6,–58), (7,19)} D. {(–2,–18), (4,37), (5,15)}
Just to clarify, here are the answer choices:
A. {(–3,–17), (4,11), (7,19)}
B. {(3,22), (2,3), (8,27)}
C. {(4,29), (–6,–58), (7,19)}
D. {(–2,–18), (4,37), (5,15)}
And all of the points in the set must satisfy y ≤ 8x – 3.
The only way is to go through each answer choice, eliminating each that is wrong.
A) -17 ≤ -3*8-3
-17 ≤ -21 ✘
B) 22 ≤ 3*8-3
22 ≤ 21 ✘
C) a) 29 ≤ 8*4-3
29≤29 ✔
b) -58 ≤ 8*(-6)-3
-58 ≤ -49 ✔
c) 19 ≤ 7*8-3
19 ≤ 53 ✔
It becomes clear that the answer is C. But just to make sure, we must check D to make sure C is really the answer.
D) -18 ≤ 8(-2)-3
-18 ≤ -19 ✘
That means that C is the answer.
Final answer:
After evaluating each set of points for the inequality y ≤ 8x – 3, it is found that set C satisfies the inequality for all its points, making it the correct set of points containing the solutions to the inequality.
Explanation:
The student's question is related to solving a linear inequality, specifically finding which set of points satisfies the inequality y ≤ 8x – 3.
To find the correct set of points that contain the solutions to this inequality, we must check each pair of (x, y) coordinates provided in the options. A coordinate pair is a solution to the inequality if substituting the x and y value into the inequality makes it a true statement.
For (-3, -17): -17 ≤ 8*(-3) – 3, which simplifies to -17 ≤ -24 – 3. Since -17 is not less than or equal to -27, this pair is not a solution.For (4, 11): 11 ≤ 8×4 – 3, which simplifies to 11 ≤ 32 – 3. Since 11 ≤ 29, this pair is a solution.For (7, 19): 19 ≤ 8×7 – 3, which simplifies to 19 ≤ 56 – 3. Since 19 ≤ 53, this pair is a solution.B. {(3,22), (2,3), (8,27)}
C. {(4,29), (–6,–58), (7,19)}
D. {(–2,–18), (4,37), (5,15)}
After checking each set, we can conclude that set C contains all the solutions to the inequality y ≤ 8x – 3.
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
can somebody help me on these two
to find the slope for the first one, use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]
(It's the slope formula)
so... [tex]3=y2, 3=y1, 2=x2, 10=x1[/tex]
then plug in... [tex]\frac{3-3}{2-10} =\frac{0}{-8} = 0[/tex]
this line has a slope of 0
As for the miles problem, to find mph, the miles have to be at 1.
so... [tex]4x=242\\x=60.5[/tex]
therefore, he drove 60.5 mph
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
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)
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?
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]