Find all x-intercepts of the following function. Write your answer or answers as
coordinate points. Be sure to select the appropriate number of x-intercepts.
f(x)
3x + 30
25x2 - 49
Answers
Given: The function below
[tex]f(x)=\frac{3x+30}{25x^2-49}[/tex]To determine: All x-intercepts of the given function
The x-intercept is a point where the graph crosses the x-axis
We would substitute the function equal to zero and find the value of x
[tex]\begin{gathered} f(x)=\frac{3x+30}{25x^2-49},f(x)=0 \\ \text{Therefore} \\ \frac{3x+30}{25x^2-49}=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}[/tex][tex]\begin{gathered} 3x=-30 \\ \frac{3x}{3}=\frac{-30}{3} \\ x=-10 \end{gathered}[/tex]Therefore, the coordinate of the x-intercept is (-10, 0)
Related Questions
Enter the missing values in the area model to find 10(8y + 5)+510BoyAccording to the model above, 10(8y + 5) =Submit Answeatte
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Note you have to use the value outside the bracket to multiply the inner value.
-8(4 p -1)-7 p+8( p+1)
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-31p + 16
Explanation:
-8(4 p -1) - 7p+8( p+1)
Open the bracket:
-8(4p) -8(-1) - 7p +8(p) +8(+1)
Simplify:
-32p + 8 - 7p + 8p + 8
Note: the multiplication of opposite sign gives negative number. While multiplication of same sign gives positive number
Collect like terms:
= -32p - 7p + 8p + 8 + 8
= -31p + 16
Elana has 80 unit squares. What is the volume of the largest cube she can build with them? Need to show work to explain to my son, having a hard time with this.
Answers
Answer: The largest cube has volume of 64 cubic units, and the sides are 4 units long.
Step-by-step explanation:
Elena has 80 unit cubes and she has to build the largest cube using the unit cubes she has
Unit cube has a dimension of 1 unit on each side (Cube has all sides equal)
To make the largest cube, she needs to calculate the maximum volume which is near 80 units of cubes
Therefore,
We have a cube with each side 4 units whose volume is 64 and a cube with each side 5 units whose volume is 125
Elena has only 80 unit cubes to build the maximum-sized cube
Therefore she will be able to build a cube with each side as 4 units with a volume of 64 units with 16 spare cubes
A car is purchased for 19,00. Each year it loses 25% of its value. After how many years will the car be worth 5800. dollars or less? Write the smallest possible whole number answer
Answers
5 years
Explanation
Given
Cost price = $ 19,000
Depreciation yearly is % 25
What to find
Time to depreciate to $ 5, 800 or less
Step- by - Step Solution
After first year St
[tex]\begin{gathered} 25\%\text{ }of\text{ 19,000} \\ \\ \frac{25}{100}\times\text{ 19,000 = 4,750} \\ \\ 19,000\text{ - 4750 = 14, 250} \end{gathered}[/tex]After the year the second year
[tex]\begin{gathered} \frac{25}{100}\text{ }\times\text{ 14, 250 = 3,562.5} \\ \\ 14,250\text{ - 3,562.5 =10, 687.5} \end{gathered}[/tex]After Third year
[tex]\begin{gathered} 25\%\text{ of 10,687.5} \\ \\ \frac{25}{100\text{ }}\times\text{ 10, 687.5 = 2,671.875} \\ \\ 10,687.5\text{ - 2,671.875 = 8,015.625} \\ \end{gathered}[/tex]After Fourth year
[tex]\begin{gathered} 25\%\text{ of 8,015.625} \\ \\ \frac{25}{100}\times\text{ 8,015.625 = 20003.906} \\ \\ 8\text{,015.625 - 20,003.906 = 6011.719} \end{gathered}[/tex]After Fifth year
[tex]\begin{gathered} 25\%\text{ of 6011.719} \\ \\ \frac{25}{100}\times\text{ 6011.719 = 1502.930} \\ \\ 6011.719-1502.930\text{ = 4508.789} \end{gathered}[/tex]Therefore after 5 years the car be worth 5800. dollars or less Therefore after 5 years the car be worth 5800. dollars or less
the net of a rectangular prism is shown below. the surface area of each face is labeled. which vakues represent the dimensions, in meters, of the rectangular prism.
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The answer is 5, 9, 10
which graph represents the solution to -1/2m>7/11
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The graph of the inequality:
(-1/2)*m > 7/11
Can be seen in the image at the end.
Which graph represents the solution for the inequality?Here we have the following inequality:
(-1/2)*m > 7/11
First, let's solve this for m, this means that we need to isolate the variable in one side of the inequality.
If we multiply both sides by -2, we get:
-2*(-1/2)*m < -2*(7/11)
Where the direction of the symbol changes because we are multiplying by a negative number.
m < -14/11
The graph of this will be an open circle at -14/11 and an arrow that goes to the left, like the one below.
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My Marjorie made for rates and 6 hours and 6 wreaths and 9 hours what is the constant of proportionality
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The constant of proportionality is computed as follows:
[tex]k=\frac{\text{number of wreaths}}{\text{ number of hours}}[/tex]Assuming that 6 wreaths correspond to 9 hours, the constant of proportionality is:
[tex]k=\frac{6\text{ wreaths}}{9\text{ hours}}=\frac{2}{3}\frac{wreath}{hour}[/tex](4, 2); slope = 3 writing linear equations given point and slope
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The standard equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0) where;
m is the slope
(x0, y0) is the point on the line
Given
(x0, y0) = (4, 2)
From the coordinate;
x0 = 4 and y0 =2
slope m = 3
Substitute the given parameters into the equation as shown;
y-2 = 3(x-4)
Hence the linear equations given the point and slope id expressed as y-2 = 3(x-4)
Help with these two questions please. Match the sentence with a word
Answers
EXPLANATION
Given that two angles form a linear pair, we can assevere that the postulate that applies is the Linear Pair Postulate.
The equation 3x + 2y = 120 models the number of passengers who can sit in a train car, where isthe number of adults and y is the number of children. Explain what the 2- and y-intercepts mean.
Answers
Explanation:
Given the equation that models the number of passengers who can sit in a car expressed as 3x + 2y = 120
x is the number of adults
y is the number of children
The x-intercept is the point where y is zero i.e. the number of adults when there is no number of children.
when y = 0
3x + 2(0) = 120
3x = 120
x = 120/3
x = 40
This means that there will be 40 adults if there are no children
The y-intercept is the point where x is zero i.e. the number of children when there is no number of adults.
when x = 0
3(0) + 2y = 120
2y = 120
y = 120/2
y = 60
This means that there will be 60children if there are no adults
In a group of 80 animals, 32 are dogs. Dogs make upwhat percent of the animals in the group?A. 32.00B. 28.6C. 35.5D. 38.00E 40.00
Answers
Let's calculate the percentage of dogs in the animal group
[tex]\begin{gathered} P=\frac{32}{80} \\ P=0.40 \\ P=40\text{ \%} \end{gathered}[/tex]The answer would be 40%.
5. Prove triangle ABD is congruent to triangle CDB. DC|AB D
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Solve the following system of equations Detailed step by step
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SOLUTION:
Step 1:
In this question, we are given the following:
[tex]\begin{gathered} 2\text{ x + y = 2 ------equation 1} \\ 4\text{ x + 3y =- 2--- -equation 2} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
The graphical solution for the two systems of equations are as follows:
CONCLUSION:
The solutions to the systems of equations are:
[tex]x\text{ = 4 , y = -6}[/tex]
Let f(x) = 2x
. Suppose that a new function g(x) is created by taking the
graph of f(x) and performing the following transformations:
• Reflection in the x-axis
• Reflection in the y-axis
• Vertical stretch by a factor of 3
• Translation up 2 units
• Translation right 3 units. [3, 2 marks]
a) Find a possible equation for g(x).
Answers
Assume that a new function g(x) is created by taking the graph of f(x) and performing the following transformations: vertical stretch by a factor of 3
What is meant by Reflection?A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure is equidistant from every point in another figure. The reflected image should be the same shape and size as the original, but it should face in the opposite direction. Translation can also occur as a result of changes in position. The original image is referred to as the pre-image, and its reflection is referred to as the image. The pre-image and image are represented by ABC and A'B'C', respectively. The coordinate system may be used in the reflection transformation (X and Y-axis).To learn more about Reflection, refer to:
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Given these points please solve this problme.
Answers
The point that belongs to the solution set is A( 4, 4)
What are inequalities?Inequalities are defined as mathematical relations involving an unequal comparison between two numbers, elements or other arithmetic expressions.
They are mostly used to compare two numbers on the number line on the basis of their sizes.
Given the inequalities;
x + y > 63x - 5y ≤ 2Make 'x' the subject from equation 1, we have;
x > 6 - y
substitute the value into equation 2, we have;
3( 6 - y) - 5y ≤ 2
expand the bracket
18 - 3y - 5y ≤ 2
collect like terms
- 8y ≤ 2 - 18
- 8y ≤ -16
Make 'y' the subject of formula
y ≤ 2
Substitute the value in equation 3
x > 6 - 2
x > 4
Hence, the point is A( 4, 4)
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4y+3+6xWhat is the numerical coefficient of the first term?What is the constant term?
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We are given the following expression:
[tex]4y+3+6x[/tex]The numerical coefficient is the number that multiplies a variable, in this case, the first variable is "y" and the numerical coefficient is 4.
The constant in an expression is the number that does not multiply any variable, in this case, the constant is 3.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q5
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ANSWER:
STEP-BY-STEP EXPLANATION:
We can determine the domain and range of the function, knowing that the domain is the interval of values in x and the range is the interval of values in y.
Therefore:
[tex]\begin{gathered} D=\lbrack-5,5\rbrack \\ R=\mleft[-5,\frac{25}{17}\mright] \end{gathered}[/tex]When a function is inverted, the domain and range are inverted, therefore:
[tex]\begin{gathered} D=\mleft[-5,\frac{25}{17}\mright] \\ R=\lbrack-5,5\rbrack \end{gathered}[/tex]Which means that the inverted function goes from -5 to 25/17 in x and from -5 to 5 in y.
In addition to this we must take into account that when the inverse function is done, in most cases a reflection is made in y = x.
The only graph that meets all of the above is graph A
Solve, graph and write the solution in interval notation: |2x−1|>5
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Given: the inequality is,
[tex]|2x-1|>5[/tex]To solve the inequality,
[tex]\begin{gathered} |2x-1|>5 \\ -5<2x-1<5 \\ -5+1<2x<5+1 \\ -4<2x<6 \\ -\frac{4}{2}The graph will conntain a region -2The graph for the giev inequality is,
The area of a circle is about 167.3306 square inches. The circle's circumference is ____ inches.Use 3.14 for π.
Answers
The area of a circle can be calculated using this formula:
[tex]A=\pi r^2[/tex]Where "r" is the radius of the circle.
The circumference of a circle can be found using this formula:
[tex]C=2\pi r[/tex]Where "r" is the radius of the circle.
In this case you know that the area of this circle is:
[tex]A\approx167.3306in^2[/tex]Then, you can substitute this value into the first formula and solve for "r". Use:
[tex]\pi=3.14[/tex]Then:
[tex]\begin{gathered} (167.3306in^2)=(3.14)r^2 \\ \\ \frac{(167.3306in^2)}{3.14}=r^2 \\ \\ r=\sqrt[]{(\frac{167.3306in^2}{3.14})} \\ \\ r=7.3in \end{gathered}[/tex]Now you can substitute this value into the formula for calculate the circumference of a circle:
[tex]\begin{gathered} C=(2)(3.14)(7.3in) \\ \end{gathered}[/tex]Finally, evaluating, you get:
[tex]C=45.844in[/tex]The answer is:
[tex]45.844in[/tex]Solve for the unknown: 6(B+2) = 30
Answers
The unknown is B
[tex]6(B+2)=30[/tex][tex]\begin{gathered} 6B+12=30 \\ 6B+12-12=30-12 \\ 6B=18 \\ B=\frac{18}{6} \\ B=3 \end{gathered}[/tex]estimate 2,829 divided by 33=?
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Answer: 100
Step-by-step explanation:
Calculate it and 85.7272727273 is closer to 100 so its 100
2064 is divisible by 2, 4 and 8 true or false
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Explanation:
2064/2 is 1032
1032/2 is 258
And 258 is divisible by 2 so 2 and 2x2 and 2x2x2.
describe the center and spread of the data using the more appropriate status either the mean median range interquartile range or standard division
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name a 2 digit odd number that is composite
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We should know that:
All the odd integers which are not prime are odd composite numbers. Examples of composite odd numbers are 9, 15, 21, 25
3) Describe what ALL graphs of proportional relationships have in common
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SOLUTION
What all graphs of proportional relationships have in common is a straight line.
This line is straight, no curves or bends. This straight line passes through the origin at an intersection of
[tex](0,0)[/tex]Hence, the answer is "A straight line that passes through the origin and goes at a constant rate".
find the circumference of the circle L. Write your answer as a decimal, rounded to the nearest hundredth. the circumference is blank feet
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Let us call C the circumference of the circle.
We know that the ratio of angle to circumference must be
[tex]\frac{106}{360}=\frac{1.25}{C}[/tex]cross multipication gives
[tex]106(C)=360\cdot1.25[/tex]Dividing both sides by 106 gives
[tex]C=\frac{360\cdot1.25}{106}[/tex][tex]C=4.25[/tex]which is our answer!
A student is trying to solve the set of two equations given below:Equation A: x + z = 6Equation B: 3x + 2z = 1Which of the following is a possible step used in eliminating the z-term
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Answer:
multiply equation A by -2
Identify the slope and y-intercept of the line y=−2x−1.
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Given the equation of the line:
[tex]y=-2x-1[/tex]The given equation as the slope-intercept form: y = m * x + b
where m is the slope and b is the y-intercept
the y-intercept is the value of y when x = 0
By comparing the given equation with the slope-intercept form
So,
The slope = m = -2
The y-intercept = b = -1
the point of y-intercept = ( 0, -1 )
what is the area of a circle with the radius of 10, then rounding the answer to the nearest tenth?
Answers
Given a circle with a radius = r = 10 in
The area of the circle is given by the following formula:
[tex]A=\pi\cdot r^2[/tex]Substitute with r= 10
so, the area will be:
[tex]A=\pi\cdot10^2=\frac{22}{7}\cdot10^2=\frac{22}{7}\cdot100=314.2857[/tex]Rounding the answer to the nearest tenth:
So, the answer will be area = 314.3 square inches
Professor Torres is stucked in a burning building. He is leaning to the window on the 5th floor which is 60feets above the ground. For stability, the firefighter have to place the bottom of their ladder 15feet from the wall of the building. How long does the ladder needs to be to reach the window on the 5th floor and save professor Torres? round to 2 decimal place
Answers
The situation forms the right triangle above:
Where x is the length of the ladder.
Apply the Pythagorean theorem:
c^2 = a^2 +b^1
where:
c = hypotenuse = longest side = x
A &b = the other 2 legs of the triangle
Replacing:
x^2 = 60^2 + 15^2
Solve for x
x^2 = 3,600 + 225
x^2 = 3,825
x =√3,825
x = 61.85 ft