Final answer:
To simplify the fourth root of a non-perfect power, use a calculator to raise the number to the power of 0.25, or calculate the square root twice. For non-integer powers, calculate roots with corresponding fractional exponents. Request assistance from your instructor if necessary.
Explanation:
Simplifying the Fourth Root of Non-Perfect Powers
When simplifying the fourth root of a number that is not a perfect fourth power, you can utilize the power function on a calculator. This involves raising numbers to the power of 0.25, which equates to calculating the fourth root. For example, using the y* button (or equivalent) you can calculate the fourth root of any number by raising it to the power of 0.25. This is analogous to how raising a number to the 0.5 power gives us the square root of that number. If your calculator doesn't have this function, another technique is to calculate the square root of the number twice, since the fourth root is essentially the square root of the square root.
To work through a non-integer power, like 31.7, you can find the tenth-root of 3 by raising it to the power of 0.1 and then raise the result to the 17th power. Similarly, for expressions with fractional exponents like x0.5, you can interpret this as the square root of x. Understanding that fractional powers represent roots can help in simplifying complex expressions without a calculator as well.
If you are dealing with equilibrium problems or other scenarios that require finding roots of numbers, it's crucial to be comfortable with these techniques. If you are unsure about how to perform these operations, don't hesitate to ask for assistance from your instructor. Developing a natural and forgiving relationship with numbers, and only representing precision as needed, is also an important aspect of working with mathematical problems.
Which two equations would be most appropriately solved by using the zero product property? Select each correct answer. 4x² = 13 0.25x2+0.8x−8=0 −(x−1)(x+9)=0 3x2−6x=0
Answer:
−(x−1)(x+9)=0
And..
3x2−6x=0
Step-by-step explanation:
Final answer:
The two equations most appropriately solved by using the zero product property are −(x−1)(x+9)=0 and 3x²−6x=0, as they can be directly factored into a product of terms equaling zero.
Explanation:
The question involves finding which two equations would be most appropriately solved by using the zero product property. The zero product property states that if the product of two numbers is zero, then at least one of the multiplicands must be zero. Therefore, equations that can be factored into a product of terms equaling zero can be solved using this property.
−(x−1)(x+9)=0: This equation is already in a factored form and directly applies the zero product property. Set each factor equal to zero and solve for x: x−1=0 or x+9=0, which gives x = 1 or x = −9.3x²−6x=0: This equation can be factored as 3x(x−2)=0. By applying the zero product property, set 3x=0 and x−2=0, solving for x gives x = 0 or x = 2.The other options, 4x² = 13 and 0.25x²+0.8x−8=0, are not immediately in a form that uses the zero product property without further manipulation or do not directly apply to this property.
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
Answer:
[tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].
Step-by-step explanation:
We are given a geometric sequence { -16, 4, -1, .... }
i.e. [tex]a_{1} =-16[/tex], [tex]a_{2} =4[/tex], [tex]a_{3} =-1[/tex], ...
We will first find the common ratio 'r'.
Now, [tex]r=\frac{a_{n}}{a_{n-1}}[/tex]
i.e. [tex]r=\frac{a_{2}}{a_{1}}[/tex]
i.e. [tex]r=\frac{4}{-16}[/tex]
i.e. [tex]r=\frac{1}{-4}[/tex]
Similarly, i.e. [tex]r=\frac{a_{3}}{a_{2}}[/tex]
i.e. [tex]r=\frac{-1}{4}[/tex]
So, we get that the common ratio is [tex]r=\frac{-1}{4}[/tex].
Now, the recursive formula for the geometric sequence is given by,
[tex]a_{n} =r \times a_{n-1}[/tex]
i.e. [tex]a_{n} =\frac{-1}{4} \times a_{n-1}[/tex]
i.e. [tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].
Hence, the recursive formula for this sequence is [tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].
If you add 0.43 to a certain number then subtract 0.58 from the result and then another 4.04, you’ll get 30.3. What is the certain number?
Please show how you did it.
Answer:
34.49
Step-by-step explanation:
You do it reverse
30.3+4.04=34.34
34.34+0.58=34.92
34.92-0.43=34.49
WILL GIVE BRAINLIEST!!!!!
1. Use the parabola tool to graph the quadratic function f(x)=x2+10x+16 . Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
2. Use the parabola tool to graph the quadratic function f(x)=−(x−3)(x+1) .
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
3. Use the parabola tool to graph the quadratic function f(x)=−x2+4.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
4. Use the parabola tool to graph the quadratic function f(x)=2x2+16x+30 .
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
5. Select ALL the statements that are true for the graph of y=(x+2)2+4 .
The graph has a maximum.
The graph has a minimum.
The vertex is (2, 4) .
The vertex is (−2, 4) .
1. f(x)=x²+10x+16
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(As, a>0 the parabola is open upward), b=10. by putting the values.
-b/2a = -10/2(1) = -5
f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9
So, Vertex = (-5, -9)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).
Now find x-intercept put y=0 in the above equation. 0= x²+10x+16
x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
2. f(x)=−(x−3)(x+1)
By multiplying the factors, the general form is f(x)= -x²+2x+3.
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.
-b/2a = -2/2(-1) = 1
f(-b/2a)= f(1)=-(1)²+2(1)+3= 4
So, Vertex = (1, 4)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).
Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.
-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
3. f(x)= −x²+4
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=0. by putting the values.
-b/2a = -0/2(-1) = 0
f(-b/2a)= f(0)= −(0)²+4 =4
So, Vertex = (0, 4)
Now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).
Now find x-intercept put y=0 in the above equation. 0= −x²+4
−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
4. f(x)=2x²+16x+30
Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(As, a>0 the parabola is open upward), b=16. by putting the values.
-b/2a = -16/2(2) = -4
f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2
So, Vertex = (-4, -2)
Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).
Now find x-intercept put y=0 in the above equation. 0=2x²+16x+30
2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
5. y=(x+2)²+4
The general form of parabola is y=a(x-h)²+k , where vertex = (h,k)
if a>0 parabola is opened upward.
if a<0 parabola is opened downward.
Compare the given equation with general form of parabola.
-h=2 ⇒h=-2
k=4
so, vertex= (-2, 4)
As, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.
The graph is attached below.
Here are a bunch of CORRECT answers, your answer is somewhere in there. For the first CORRECT answer the second point is -5,-9. Don't make the same mistake I did on question 3, but it still shows the correct answer. I love to help.
Leyla drops a penny from a height of 150 m.
How long will it take the penny to hit the ground?
Use the formula h(t)=−4.9t2+vot+h o, where vo is the initial velocity and h o is the initial height. Round to the nearest tenth of a second.
Answer:
I believe its 5.5
Step-by-step explanation:
Which of the following shows the graph of y = 4x + 3?.
its the first graph
A
To find the graph of the equation y = 4x + 3, plot the y-intercept at (0,3) and use the slope of 4 to plot additional points. Connect these points to form a straight line that slopes upward to the right, reflecting a positive slope.
The student has asked to identify the graph of the equation y = 4x + 3. This is an equation of a straight line where the slope (m) is 4 and the y-intercept (b) is 3. According to the properties of linear equations, for every increase of 1 on the x-axis, the value of y will increase by the slope value, which is 4 in this case. The graph will intersect the y-axis at 3, which is the y-intercept.
To graph this line, you can start by plotting the y-intercept at (0,3) on the graph. Then, use the slope to determine the next point by moving 4 units up for every 1 unit you move to the right. Repeat this process with several values of x to construct a table, for instance, at x=1, y=7, at x=2, y=11, etc. These points are then plotted and connected with a straight line to represent the graph of the equation.
Referring to Figure 12.4, we can see that the line would match figure (a) which shows a line that slopes upward to the right, because our b value (slope) is greater than 0.
10 Michael has a drawer with 8 pairs of black socks and 12 pairs of white socks. Without looking he takes a white pair of socks out of the drawer. What is the probability that the next pair he takes out is black?
Gina sells 216 cakes in the ratio small :medium:large 5:7:12. The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake. Her total profit id £648.45. Work out the profit for one small cake.
Answer:
The profit for one small cake is £1.31.
Step-by-step explanation:
It is given that that Gina sells 216 cakes in the ratio small:medium:large 5:7:12.
[tex]5+7+12=24[/tex]
Number of small cakes = [tex]216\times \frac{5}{24}=45[/tex]
Number of medium cakes = [tex]216\times \frac{7}{24}=63[/tex]
Number of large cakes = [tex]216\times \frac{12}{24}=108[/tex]
The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake.
Let the profit for one small cake be x. So the profit for one medium and large cake are 2x and 3x respectively.
Her total profit id £648.45.
[tex]45\times x+63\times 2x+108\times 3x=648.45[/tex]
[tex]45x+126x+324x=648.45[/tex]
[tex]496x=648.45[/tex]
Divide both sides 496.
[tex]\frac{496x}{496}=\frac{648.45}{496}[/tex]
[tex]x=1.30735887097[/tex]
[tex]x\approx 1.31[/tex]
Therefore the profit for one small cake is £1.31.
What is the area of a triangle that has a base of 3 feet and a height of 6 feet?
A: 18 ft^2
B: 18 ft C: 9 ft^ 2 D: 4.5 ft^2
The formula of area of triangle is given by
[tex] A= \frac{1}{2} b*h [/tex]
Where b is the base and h is the height .
In the given question, base ,b = 3 feet
Height, h= 6 feet
Substituting the values of b and h in the formula, we will get
[tex] A = \frac{1}{2}*3*6 = 9 ft^2 [/tex]
Correct option is C .
Answer:
9 ft^ 2
Step-by-step explanation:
A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
PLEASE ANSWER
Answer:The answer is B !
Step-by-step explanation:
A translation is a rigid translation that changes the location of a figure without a net reflection or rotation
The option that gives the correct image of the preimage DEFG, which is D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3), is; The second diagram
Please find attached a diagram showing the preimage and the image
The reason why the selected option is correct is given as follows
The given translation is T₍₋₁, ₂₎(x, y)
Coordinates of the pre-image are D(-1, 3), E(4, 3), F(4, 1), and G(-1, 1)
Required:
To find the image formed following the translation
Solution:
To translate a preimage given the measure of the translation of the x and y-values, in the form T₍₋₁, ₂₎(x, y), '-1' is added to the x-values, and '2' is added to the y-values, as follows
D(-1, 3) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] D'(-1 - 1, 3 + 2) = D'(-2, 5)E(4, 3) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] E'(4 - 1, 3 + 2) = E'3, 5)F(4, 1) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] F'(4 - 1, 1 + 2) = F'(3, 3)G(-1, 1) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] G'(-1 - 1, 1 + 2) = G'(-2, 3)The coordinates of the vertices of the image are D'(-2, 5), E'(3, 5), F'(3, 3), and G'(-2, 3)
The image of DEFG is the second diagram, D'E'F'G'.
Please find attached the diagram of the image of the preimage DEFG constructed with dashes
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A system of linear equations is shown below. 2x + 4y = 10 3x – y = 8 marla is attempting to prove that by replacing 2x + 4y = 10 with a different equation it will sometimes produce a new system of equations with the same solution. marla plans on multiplying 2x + 4y = 10 by 2 and then adding the results to the equation 3x – y = 8 in order to create a new equation. marla claims that the new equation that she will replace 2x + 4y = 10 with is 7x + 7y = 12. is marla correct?
No, Marla is not correct. The correct new equation is 4x + 8y = 20.
Explanation:No, Marla is not correct. To create a new equation that represents the same system of equations, we need to perform the same mathematical operation on both sides of the equation. In this case, Marla multiplied the left side of the equation by 2, but not the right side. To maintain equality, we need to multiply both sides of the equation by the same constant. Therefore, the correct new equation would be 4x + 8y = 20.
the radius of a circular park is 120 m. to nearest meter, what is the circumference of the park.
How many distinct pairs of perfect squares differ by 35? (the pair $a, b$ is the same as the pair $b, a$.)?
Answer:
2
Step-by-step explanation:
Bianca planted seeds to grow zinnias, sunflowers, and marigolds. After several weeks, 18 out of 50 zinnia seeds, 12 out of 30 sunflower seeds, and 14 out of 40 marigold seeds grew into plants. Drag the names of the plants in order from the least percentage of plants that grew to the greatest percentage of plants that grew.
Jane plans to invest $500 at 8.25% interest, compounded continuously. After 14 years, how much money has she accumulated? Has her money doubled or tripled?
After 14 years, Jane has accumulated approximately $1587.45, which means her initial investment of $500 has more than tripled due to the power of compound interest at a rate of 8.25%, compounded continuously.
Jane plans to invest $500 at 8.25% interest, compounded continuously. To find out how much money she has accumulated after 14 years, we use the formula for continuous compounding: [tex]A = Pe^{rt}[/tex], where:
For Jane's investment:
P = $500
r = 8.25% or 0.0825 (as a decimal)
t = 14 years
Plugging these values into the formula gets us:
[tex]A = 500e^{0.0825*14}[/tex]
Calculating this gives us:
[tex]A \approx 500e^{1.155} \approx 500 * 3.1749 \approx $1587.45[/tex]
Jane's money has more than tripled in 14 years. It has not quadrupled, but it has significantly grown beyond double the original investment.
A garden is in the shape of a square. the area of the garden is 178 square meters. the exact length of a side of the garden is between which two lengths?
Find the area of the triangle. Round the answer to the nearest tenth.
A.
27.1 square units
B.
29.0 square units
C.
178.3 square units
D.
356.6 square units
Answer:
The correct option is C.
Step-by-step explanation:
Given information: AB=20.4, BC=17.7 and ∠ B = 99 °.
It two sides and their inclined angle is given then the area of the triangle is
[tex]A=\frac{1}{2}ab\sin C[/tex]
Where, a and b are two sides of a triangle and C is their inclined angle.
The area of given triangle is
[tex]A=\frac{1}{2}\times 20.4\times 17.7 \sin 99^{\circ}[/tex]
[tex]A=178.317253[/tex]
[tex]A\approx 178.3[/tex]
The area of the triangle ABC is 178.3 square units. Therefore the correct option is C.
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Which of the following best describes the intersection of two planes? (Points : 5)
line
line segment
point <
ray
I think its Point?
marika is training for a track race She starts by sprinting 100 yards . She gradually increases her distance , adding 4 yards a day for 21 days how far does she sprint on day 21
using an=100+(n-1)4
Answer:
180 yards on day 21
Step-by-step explanation:
just took on A P E X !!
Factor 20x2 + 25x – 12x – 15 by grouping. 1. Group terms with common factors. 2. Factor the GCF from each group. 3. Write the polynomial as a product of binomials.
Answer:
(5x - 3) • (4x + 5)
Step-by-step explanation:
What is the area of a trapezoid that has bases of 1feet and 14 inches and a height of 3 inches? A 43.5 in.^2 B 87 in.^2 C 22.9 in.^2 D 3.6 in.^2
Answer:
Option A. [tex]43.5\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=(1/2)(b1+b2)h[/tex]
we have
[tex]b1=1\frac{1}{4}\ ft[/tex]
[tex]b2=14\ in[/tex]
[tex]h=3\ in[/tex]
Convert feet to inches first
Remember that
[tex]1\ ft=12\ in[/tex]
so
[tex]1\frac{1}{4}\ ft=\frac{5}{4}\ ft=12*\frac{5}{4}=15\ in[/tex]
substitute in the formula
[tex]A=(1/2)(15+14)3=43.5\ in^{2}[/tex]
Answer:
43.5 in^2
Step-by-step explanation:
Compute the requested value to hundredths of a percent. Choose the correct answer. You see a used car you wish to buy. The dealer quotes you a price of $1,595. You have a Blue Book quotation of $1,435 for the same model and year. How much greater (%) is the dealer's price from the Blue Book? It is _____%.
Answer:
11.15
Step-by-step explanation:
Erick, Mia, and Isabelle golfed 9 holes. Erick scored 10 more than Mia, and Isabelle scored 16 less than twice Mia's score. Use the drop-down menus to complete the statements about the expression that represents the scenario. What does the expression x + x + 10 + 2x – 16 represent from the given scenario? What does the variable in the expression represent? What is the expression in simplified form? What is the constant in the simplified expression?
Answer:
1. The total score of all three players.
2. Mia's score.
3. 4x-6\
4. -6
The mathematical expression from the scenario represents the total golf scores of Erick, Mia, and Isabelle. The variable represents Mia's score, and the simplified expression is 4x - 6, with -6 being the constant.
Explanation:From the given scenario, the expression x + x + 10 + 2x - 16 represents the total score of Erick, Mia, and Isabelle. The variable 'x' in this expression represents Mia's golf score, as other scores are dependent on it.
To simplify the expression, we group like terms: x (Mia's score) + x (Erick's score, which is 10 more than Mia's) + 2x (Isabelle's score, which is 16 less than twice Mia's) - 16. Simplifying this, we get 4x - 6. So, the simplified expression is 4x - 6.
The constant in the simplified expression is -6. This is the value that is added or subtracted to the variable's value, irrespective of its value.
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Find X. This is Big Ideas Geometry Chapter 9.3
The value of x of the triangle is: x = 24 units
How to find the length of similar triangles?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
Thus, the length of the base is:
c² = 30² + 40²
c² = 2500
c = √2500
c = 50 units
Using the concept of similarity ratio, we have:
30/50 = x/40
Cross multiply to get:
50x = 1200
x = 24 units
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Find the balance in the account after the given period. $3500 deposit 6.75% compounded monthly, after 6 months
Given that z20 = –2 and z50= – 1, which of the following do you know?
1.) The variance is 10.
2.) The standard deviation is 30.
3.) The mean is 80.
4.) The median is 40.
5.) The data point x=20 is 2 standard deviations form the mean
6.) The data point x=50 is 1 standard deviation from the mean
7.) The data point x=45 has a z-valued of 1.5
Answer:
it is 2;3;5;6
Step-by-step explanation:
Given that z20 = –2 and z 50= –1, which of the following do you know?
The variance is 10.
The standard deviation is 30.
The mean is 80.
The median is 40.
The data point x = 20 is 2 standard deviations from the mean.
The data point x = 50 is 1 standard deviation from the mean.
The data point x = 45 has a z-value of 1.5.
answer2356 on edge
The solution is, it is 2;3;5;6.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
here, we have,
Given that z20 = –2 and z 50= –1, which of the following do you know?
The variance is 10.
The standard deviation is 30.
The mean is 80.
The median is 40.
The data point x = 20 is 2 standard deviations from the mean.
The data point x = 50 is 1 standard deviation from the mean.
The data point x = 45 has a z-value of 1.5.
so, we get,
answer2, 3, 5, 6 on edge.
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What transformation has changed the parent function f(x) = 3(2)x to its new appearance shown in the graph below?
exponential graph passing through point 0, 5.
f(x) + 2
f(x) + 4
f(x + 2)
f(x + 4)
Chris wants to make an enclosed rectangular area for a mulch pile. She wants to make the enclosure in such a way as to use a corner of her back yard. She also wants it to be twice as long as it is wide. Since the yard is already fenced, she simply needs to construct two sides of the mulch pile enclosure. She has only 15 feet of material available. Find the dimensions of the enclosure that will produce the maximum area
Chris should construct the enclosure with a width of 5 feet and a length of 10 feet, using her 15 feet of fencing material, which will result in a maximum enclosed area of 50 square feet.
Chris wants to construct an enclosed rectangular area for a mulch pile and use her backyard's corner fence effectively, thereby constructing only two sides of the mulch pile enclosure. She has 15 feet of fencing material to use and wants the length of the rectangular enclosure to be twice the width. To find the dimensions that will produce the maximum area, we can set up an equation.
Let x represent the width (in feet) and 2x represent the length (in feet), since the length is twice the width.
Since Chris is using the corner of the yard, she only needs to construct two sides of the fence.
Therefore, the amount of fencing material she will use (perimeter of two sides) is given by the equation x + 2x = 15, which simplifies to 3x = 15.
Solving for x, we find that x = 5 feet. Thus, the width of the enclosure is 5 feet, and the length is twice that, or 10 feet.
The maximum area that Chris can enclose is therefore 5 ft imes 10 ft = 50 square feet.
A car travels 200 miles in the same time that a train travels 300 miles. The speed of the train is 20 miles per hour more than the speed of the car. Which equation could be used to determine the speed of the car, r, in miles per hour?