Solve for X. Show work
The value of x in the figure is 5
How to solve for x?From the figure, we have the following parameters are:
NM = 9
ML = 2x - 7
NL = x + 7
This means that
NL = NM + ML
So, we have:
x + 7 = 9 + 2x - 7
Collect the like terns
x - 2x = 9 - 7 - 7
Evaluate
-x = -5
This gives
x = 5
Hence, the value of x in the figure is 5
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A truck can be rented from Company A for $90 a day plus $0.40 per mile. Company B charges $60 a day plus $0.70 per mile to rent the same truck.
Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in a day at which the rental costs for Company A and Company B are the same will be 10 miles.
How to calculate the value?Let the number of miles be represented by x.
Therefore the equation for the first company will be 90 + 0.4m
The equation for the second company will be 60 + 0.7m
Therefore, we will equate them. This will be:
90 + 0.4m = 60 + 0.7m
Collect like terms
90 - 60 = 0.7m - 0.4m
0.3m = 30
m = 30/0.3
m = 10
The number of miles will be 10 miles.
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Camille wants to crochet a blanket for her new baby cousin. her pattern calls for 900 yards of thick, soft wool. she already has 200 feet of wool left from another project. at the craft store, she notices that each ball has 500 feet of wool. how many balls of wool should she buy?
Camille need 5 balls of wool to crochet a blanket for her new baby cousin.
Unitary Method:
Unitary method is the method in which the value of a unit quantity is first calculated to get the value of any quantity is called the unitary method.
Given,
Camille wants to crochet a blanket for her new baby cousin. her pattern calls for 900 yards of thick, soft wool. she already has 200 feet of wool left from another project. at the craft store, she notices that each ball has 500 feet of wool.
Here we need to find the number of wool balls she need.
Let us consider x be the amount of wool balls she need.
Then,
wool needed - 900 yards
We know that,
1 yard = 3 feet
Then 900 yards will be equal to
=> 900 x 3 = 2700 feet
Now, She has - 200 feet
And we know that,
each ball at store contains - 500 feet
So it can be written as,
=> 200 + 500x = 2700
=> 500x = 2500
=> x = 2500/500
=> x = 5
Hence she need to buy 5 balls of wool from the store to get the required length of wool.
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What are the coordinates of the point on the
directed line segment from (4, 3) to (9, 8) that
partitions the segment into a ratio of 2 to 3?
The required coordinates are (6, 5).
Let A denotes the point (4, 3), and B denotes the point (9, 8).
Let C denote the point which divides the line segment AB in the ratio of 2:3.
The distance between A(4, 3) and B(9, 8) is given by
AB = √{(x₂ - x₁)² + (y₂ -y₁)²}
= √{(9 - 4)² + (8 - 3)²
= √{5² + 5²}
= √(2×5²)
= 5√2
We have AC + BC = AB
AC and BC are in the ratio 2:3.
Therefore 2x + 3x = AB
⇒5x = 5√2
⇒x = √2.
Therefore, AC = 2√2 and BC = 3√2.
Using the distance formula,
AC = √{(x - 4)² + (y - 3)²}
⇒ 2√2 = √{(x - 4)² + (y - 3)²}
⇒ √(2² + 2²) = √{(x - 4)² + (y - 3)²} (taking the 2 inside the square root.)
⇒ x - 4 = 2 ⇒ x = 6
⇒ y - 3 = 2 ⇒ y = 5.
Therefore the required coordinates are (6, 5).
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If a 3ft stick in the ground cast a shadow of 1. 2ft what is the height of a tree that cast a shadow that is 14. 16
Answer: The height of the tree is 35.4 ft.
Step-by-step explanation:
14.16/1.2 = 11.8
3 * 11.8 = 35.4
Joann works in a publicity office at the state university. she is paid $ 13.00 an hour for the first 35 hours she works each week and $ 19.50 an hour for every hour after that. if she makes $ 572.00 one week, how many hours did she work?
Joann worked for 64 hours in week.
Let the number of hours she work be x. The payment for first 35 hours will be added with the multiple of number of extra hours and payment for the same.
Forming the equation according above mentioned statement :
13 + 19.5x = 572
Solving the equation to find the number of hours worked by Joann
Shifting 13 to Right Hand Side of the equation
19.5x = 572 - 13
Performing subtraction on Right Hand Side of the equation
19.5x = 559
Shifting 19.5 to Right Hand Side of the equation at denominator
x = 559 ÷ 19.5
x = 28.67 hours
Rounding off the number of hours, we get the value = 29
So, Joann worked for 29 extra hours. To find the total number of hours she worked, we will simply add her working hours.
Total number of hours Joann worked = 35 hours + extra hours
Total number of hours Joann worked = 35 + 29
Total number of hours Joann worked = 64 hours
Hence, Joann worked for 64 hours in week.
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Lucy rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 10.
Answer:
Step-by-step explanation:
Discussion
The numbers on each die are 1 to 6.
They are all equally likely to turn up. There are 36 possibilities in all 6*6
So getting a 10 can be done in 3 ways.
6 + 4 = 10
4 + 6 = 10
5 + 5 = 10
You can't get 10 any other way.
So of the 36 ways of throwing 2 dice, only 3 will work.
Answer
P(10)= 3/36 = 1/12 = 0.0833333...
What is
greater than
-3/8?
Answer:
give a situation where you are adapted a holistic view in looking at a problem or situation: my own
I need help right now!
Which expression is equivalent to 5(−2.3b − 4.1) − (7b + 0.7)?
−18.5b − 21.2
18.5b − 21.2
−18.5b − 3.4
18.5b + 3.4
Answer: B (18.5b-21.2)
The required expression −18.5b − 21.2 is equivalent to the given expression which is the correct answer that would be option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have been given the expression below as
5(−2.3b − 4.1) − (7b + 0.7)
Open the parentheses and apply the distributive property of multiplication,
⇒ −2.3b × 5 − 4.1 × 5 − 7b - 0.7
⇒ -11.5 - 20.5 − 7b - 0.7
Rearrange the likewise terms and apply the arithmetic operation,
⇒ −18.5b − 21.2
Hence, the required expression −18.5b − 21.2 is equivalent to the given expression.
Thus, the correct answer would be an option (A).
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determine the position of each hidden term. -14 is the _th term of 2 1/5, 2 , 1 4/5
-14 is the 81th term.
What is the position of -14?The first step is to determine the relationship between the numbers in the sequence. When examined, it can be seen that the number decline by 1/5.
To confirm : 2 1/5 - 2 = 1/5
The linear equation that can be used to determine the position of a number is:
2 1/5 - 1/5(x)
Where x is the position of the number
For example, the third number is
2 1/5 - 1/5(3) = 1 4/5
Given the number, the position of the number can be determined using the above linear equation:
-14 = 2 1/5 - 1/5(x)
In order to determine the value of x, take the following steps:
Multiply through by 5
(-14 x 5) = (11/5 x 5) - (x / 5 x 5)
-70 = 11 -x
Combine similar terms: 70 + 11 = x
Add similar terms: x = 81
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Find the unit vectors that are parallet to the tangent line to the parabola y=x^2 at the point (3,9)
The unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].
What are unit vectors?Unit vectors have a magnitude of exactly one unit. They are extremely useful for a variety of reasons.In particular, the unit vectors [0,1] and [1,0] can be combined to form any other vector.To find the unit vector:
Differentiate y = x² with respect to x.
We get, dy/dx = 2x.
The slope of a tangent:
[tex]\mathrm{P}(2,4)=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{atP}(2,4)}=2 \times 2=4[/tex]
Tangent P equation is:
y - 4 = 4(x - 2)y = 4x - 4y = 4xy = 4x is the equation of a line passing through the origin O and parallel to the tangent at P.
4x = y, z = 0x/1 = y/4, z = 0This line's direction ratios are 1, 4, and 0, and its direction cosines are:
[tex]\pm \frac{1}{\sqrt{1^2+4^2+0^2}}, \pm \frac{4}{\sqrt{1^2+4^2+0^2}}, 0\\\pm \frac{1}{\sqrt{17}}, \pm \frac{4}{\sqrt{17}}, 0[/tex]
The number of unit vectors parallel to the tangent line at P(2,4) is:
[tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\bar{j}\right)[/tex]
Therefore, the unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].
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The correct question is given below:
Find the unit vectors that are parallel to the tangent line to the parabola y=x^2 at the point (2, 4).
A 10-lb bag of flour costs $3.69. A 5-lb bag costs $1.55. How much can you save if you buy the big bag instead of 2 small bags?
You will $0.29, if you will purchase 2 small bags of flour instead of 1 big bag.
What exactly is the unitary method?The unitary method is an approach that calculates the value of a specific unit utilizing the values of multiple units, in addition to determining the value of multiple units based on the value of a single unit.To figure out the value of one item, we must first divide it, and then multiply it by the number of things we want to find the value of.For the given question;
The total cost of one big bag that is 10-lb bag of flour = $3.69.
Now, the cost of one small bag that is 5-lb = $1.55.
Thus, the cost for two small bag that is 5-lb = $3.10.
The difference in the cost = big bag cost - 2 small bag costs.
The difference in the cost = $3.69 - $3.10
The difference in the cost = $0.29.
Thus, you will save $0.29 for the purchase of 2 small bags of floor instead of one big bag.
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1.) Raisins and nuts were mixed in a
bowl. If 34 of the mixture was
made up of nuts, what was the
ratio of raisins to nuts?
Answer:
8−5=3
Step-by-step explanation:
Quadrilateral BASE is located at B (3, 4), A (-2, 3), S (4, 0), and E (-2, 5). BASE was dilated with a scale factor of 5 to create B’A’S’E’. Where is A’ located? Group of answer choices
A. (-10, 15)
B. (5, 5)
C. (15, 12)
D. (10, 15)
will give brainliest
The location of the point A' after dilation is; A'(-10, 15)
What is the result of dilation transformation?We are given that the Quadrilateral BASE is located at the following coordinates;
B(3, 4), A(-2, 3), S(4, 0), and E(-2, 5).
Now, if it is dilated by a scale factor of, it means that each of the coordinates values would be multiplied by 5 to get the new coordinates as;
B'(15, 20), A'(-10, 15), S'(20, 0), and E'(-10, 25).
Thus, we can conclude that the location of the point A' after dilation is; A'(-10, 15)
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Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2, 1), B(5, 1), C(5, 6), and D(2, 6).
Given these coordinates, what is the length of side AB of this rectangle?
Does the fugue below appear to have line symmetry if so how many lines of symmetry
Answer:
It has 1 line off symmetry.
Step-by-step explanation:
it has one straight from the top point all the way down.
What is the classification for this polynomial? 6x³y³z³ + x^4y^7
A. monomial
B. binomial
C. Trinomial
2 1 Find the equation of the line that passes through the point (-4,16) and is perpendicular to the line y =
[tex] \frac{2}{5}x - \frac{1}{5} [/tex]
the equation using the slope-intercept form. Write the equation using slope intercept form
Answer: Equation using slope intercept from y= -(5/2)x +26
Step-by-step explanation:
Write an equation of the line (in slope-intercept form) that is perpendicular to the line y=(2/5)x-(1/5) and contains the point (-4,16).
The line given is y=(2/5)x-(1/5)
Which we can rewrite in y= mx+b form as
y=(2/5)x-(1/5)
So slope of this line is (2/5)
A line perpendicular will have slope = -(5/2) , Which is (1/m)
Equation of new line will be
y = -(5/2)x +b
Now we need to find b
Plug in Point (-4,16)
Replace with the (-4,16) values
16 = (5/2) (-4) +b
solve it, 16=(-10)+b
16+10=b
b=26
Equation using slope intercept from y= -(5/2)x +26
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Caleb's vegetable garden yielded 48 pounds of bell
peppers. He gave of the yield to his neighbor, Jacob.
Caleb Sold to a local restaurant He saved the rest of
the bell peppers. How many pounds of bell peppers did
he give Jacob? How many pounds did he sell? How
many pounds did he save for himself?
Answer:
16 each
Step-by-step explanation:
Since you didn't say how much of the yield Jacob gave to the restaurant or the neighbor, I'm going to assume he kept an even share and gave them each the same share.
Assuming that, we would have to divide his harvest by 3
48/3 = 16
this means that 16 went to his neighbor, 16 to the restaurant and 16 were saved for himself.
Hope this helps! ^^
If (m-1÷m)=3 , find the value of m^3 - 1÷m^3
The value of given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
Given a equation i.e.[tex]\frac{m-1}{m}[/tex]=3 and asked to calculate the value of the equation [tex]m^{3} -\frac{1}{m^{3} }[/tex]
To calculate the value of [tex]m^{3} -\frac{1}{m^{3} }[/tex] , Need to use various operations like subtraction and division)
Given .[tex]\frac{m-1}{m}[/tex]=3
⇒m-1=3m ( cross multiplies 3 and m)
⇒2m=-1( subtraction is used)
⇒m=-[tex]\frac{1}{2}[/tex]( division is used)
Thefore the value of m in the given equation i.e.[tex]\frac{m-1}{m}[/tex]=3 is -[tex]\frac{1}{2}[/tex]
⇒ [tex]m^{3} -\frac{1}{m^{3} }[/tex]
Here the value of m =-[tex]\frac{1}{2}[/tex]
Substituting the value of m in the given equation
⇒[tex](\frac{-1}{2} )^{3}[/tex]-[tex](-2)^{3}[/tex]
⇒[tex]\frac{-1}{8}[/tex]+8(addition is used)
⇒[tex]\frac{64-1}{8}[/tex]
⇒[tex]\frac{63}{8}[/tex]
Therefore, the value of the given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
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The function can be used to determine the side length, x, of a cube given the surface area of the cube, a. the function v(x) = x3 can be used to find the volume of a cube. how can these functions be combined?
The composite function or combined functions of x(A) and V(x) is V(x(A)) = (√A/6)³ option (C) is correct.
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
A function relates an input to an output.
x2 (squaring) is a function
x3+1 is also a function
Sine, Cosine, and Tangent are functions used in trigonometry.
Although part of the question is missing the question is The function x(A)= √A/6 can be used to determine the side length, x, of a cube given the surface area of the cube, A. The function V(x)= x³ can be used to find the volume of a cube. how can these functions be combined?
a. x(v(A))= sqrt x^3/6
b. V(x(A)) = sqrt x3/6
c. V(x(A))=(sqrt A/6)^3
d. x(v(A))= (sqrt A/6)^3
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For which value of a does 4 = a +| x – 4| have no solution?
-6
0
4
6
Answer:
a = 6
Step-by-step explanation:
Hello!
First, let's isolate the Absolute Value bracket.
4 = a + |x - 4|4 - a = |x - 4|Based on the definition of Absolute value, the outcome should always be a positive number. Therefore, if the product, 4 - a, is a negative number, it will have no solutions.
That means a has to be greater than 4 for it to be negative. a should be 6.
a = 6
how do you turn this root into a power?
√5
Answer:
5^(1/2)
Step-by-step explanation:
Square root means to the power of (1/2)
cube root means to the power of (1/3)
and so on
606060+28282 pls help
Answer:
634342
FACTOR:
2 x 317171
A fish swims 27 feet below sea level
Based on the information above, it can be inferred that the diver is at a depth of 36 ft below water level.
What is the final elevation of the diver?To calculate the final elevation of the diver we must take into account the depth at which he was at the beginning and the changes he made in his position.
Start point: 52 feet below water level.Modifications: Ascended 16 feet.To calculate his current position we must subtract the number of feet he ascended from the number of feet he was at at the beginning:
52ft - 16ft = 36ftBased on the above, it can be inferred that when the diver ascended to see a school of fish, he was 36 ft below the surface of the water.
Note: This question is incomplete because there is some information missing. Here is the complete information:
A scuba diver is swimming at an elevation of 52 feet below sea level. She sees a school of fish and rises 16 feet to watch the fish. What is her elevation now? A fish swims 27 feet below.
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Describe the transformation from the parent function to the graph f(x) = 3|x+1|−6
the 3 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
the x+1 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
the -6 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
Using translation concepts, we have that:
The 3 will make the parent function vertically stretch by a factor of 3.The x + 1 will make the parent function shift horizontally left 1 unit.The -6 will make the parent function shift vertically down 1 unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
g(x) = |x|.
The translated function is:
f(x) = 3|x + 1| - 6.
The multiplication by 3 means that the function was stretched vertically by a factor of 3, hence:
The 3 will make the parent function vertically stretch by a factor of 3.
At x -> x + 1, we have that the function was shifted one unit left, hence:
The x + 1 will make the parent function shift horizontally left 1 unit.
For the subtraction by 6, the function was shifted down 6 units, hence:
The -6 will make the parent function shift vertically down 1 unit.
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The volume of the cone shown in the figure below is 1/3 the volume of the cylinder. In terms of h,
what is the volume of the
cone?
Answer:
It is the last answer [tex]\frac{16\pi }{3}[/tex]
Step-by-step explanation:
the volume of the cylinder is the area of the base times the height. The area of a circle is
a = [tex]\pi r^{2}[/tex] We are give the diameter is 8. The radius is 1/2 of the diameter so the radius is 4. [tex]4^{2}[/tex] = 16
a = 16[tex]\pi[/tex] If the cone is 1/3 of that, we divide this answer by 3 to get
a = [tex]\frac{16\pi }{3}[/tex]
How can the graph rule y=2x+1 be used to predict the result for an input (x-Value) of 7
The value of y for the given input x=7 is 15.
The given function is y=2x+1.
We need to graph the given function.
How to graph the given function?Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, need some skill and some mathematical concepts to understand.
Now,
Graph the line using the slope and y-intercept, or two points.
Slope: 2
y-intercept: (0, 1)
Plot the points (0, 1) and (1, 3)
The value of y for x=7 is y=2(7)+1=15
Therefore, the value of y for the given input x=7 is 15.
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A gaming company claimed that their role-playing games take over 65 hours to complete. A sample of 300 gamers played their role-playing games and were able to complete them with a mean time of 63, hours with a standard deviation of 10 hours. Using a 1% level of significance, test the gaming company's hypothesis.
A. Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
B. Reject the null hypothesis. There is not enough evidence to oppose the gaming company's claim.
C. Fail to reject the null hypothesis. There is not enough evidence to oppose the gaming company's claim.
D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Answer:
D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Step-by-step explanation:
Let μ = mean time to complete a role-playing game.
The company claims that their role-playing games take over 65 hours to complete, so the hypotheses are:
H₀: μ = 65 H₁: μ > 65
Therefore, this is a one-tailed test.
The significance level is 1%, so α = 0.01.
Find the value of the test statistic (z):
[tex]\textsf{sample mean }\overline{x}=63,\quad \sigma=10, \quad n=300[/tex]
[tex]\implies z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}=\dfrac{63-65}{10 / \sqrt{300}}=-2\sqrt{3}=-3.4641...[/tex]
Using the “Percentage Points of The Normal Distribution” table, the critical value is z = 2.3263 meaning the critical region is Z > 2.3263.
Since z = -3.4641... < 2.3263, the observed value of the test statistic lies outside the critical region. Therefore, the result is not significant.
Conclusion
There is sufficient evidence at the 1% level of significance to fail to reject H₀ and to oppose the alternative hypothesis that the mean time to complete the role-playing game is more than 65 hours.
Answer:
A) Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Step-by-step explanation:
The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 1% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.
what fraction is equivalent to -0.5
