Part BWrite an equation that represents the sum of the measurements of angles C and D.
Answers
Solution
- The solution steps are given below:
[tex]C+D=180\degree\text{ \lparen Sum of angle on a straight line\rparen}[/tex]Related Questions
What is the graph of the solution to the following compound inequality?3-X22 or4x+2 2 10O A.-10 -9 -8 -7 -6 -5 4 -3 -2 -1 01 23456789 10O B.-10 -9 -8 -7-6 -5 -4 -3 -2 -101 2 3456789 10C.+-10 -9 -8 -7 -6 -5 -4 -3 -2 -10123+ 18 9 1045 67O D.-10 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2+8 9 10345 67
Answers
We have a compound inequality
[tex]3-x\ge2\text{ or }4x+2\ge10[/tex]And we must graph its solution.
To graph the solution we need to solve the two inequalities of the compound inequality
1. 3 - x >= 2
To solve it we must:
- Subtract 3 from both sides
[tex]\begin{gathered} 3-x-3\ge2-3 \\ \text{ Simplifying,} \\ -x\ge-1 \end{gathered}[/tex]- Multiply both sides by -1.
We must bear in mind that when we have an inequality and we multiply or divide it by a negative number, the symbols change their meaning.
[tex]\begin{gathered} -x\cdot-1\le-1\cdot-1 \\ \text{ Simplifying, } \\ x\le1 \end{gathered}[/tex]2. 4x + 2 >= 10
To solve it we must:
- Subtract 2 from both sides
[tex]\begin{gathered} 4x+2-2\ge10-2 \\ \text{ Simplifying,} \\ 4x\ge8 \end{gathered}[/tex]- Divide both sides by 4
[tex]\begin{gathered} \frac{4x}{4}\ge\frac{8}{4} \\ \text{ Simplifying, } \\ x\ge2 \end{gathered}[/tex]Finally, since the two inequalities has an 'or' means that the graph will be the graph will be the union of the solutions of each inequality
So, the correct answer is
Find the first term of the arithmetic sequence in which a76 = 375 and the common difference is 4.8.
Answers
Given:
The expression for arithmetic expression is given as,
[tex]a_{76}=375[/tex]The common difference is d = 4.8.
The objective is to find the first term of the series.
Explanation:
The general formula for the nth term of an arithmetic progression is,
[tex]a_n=a+(n-1)d\text{ . . . . .(1)}[/tex]Here, n represents the number of terms, a represents the first term
By comparing the given expression with equation (1),
[tex]n=76[/tex]To find a:
On plugging the given values in equation (1),
[tex]375=a+(76-1)4.8[/tex]On further solving the above equation,
[tex]\begin{gathered} 375=a+(75)4.8 \\ 375=a+360 \\ a=375-360 \\ a=15 \end{gathered}[/tex]Hence, the first term of the arithmetic sequence is 15.
A hiker is standing 220 feet from the base of a hill. The angle of elevation from where he is standing to the top of the hill is 29 degrees. How tall is the hill
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Which ordered pair could be removed to make this relation a function? (-5,0) (-1-3) (4,-2) (6-1)
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Answer:
We don't need to remove any ordered pair because it is a function.
Explanation:
A relation is a function if each first coordinate is related to only one second coordinate.
For example, (-5, 1), (3, 2) and (3, 7) is not a function because 3 is related to 2 and 7.
So, for the relation in the question: (-5,0) (-1-3) (4,-2) (6,-1), we don't need to remove any ordered pair because it is a function.
8. Souve sath equation by gracking, Round to the nearest tenth.Z 4B = -7%0-7-6, -16,-11,5
Answers
Step 1: Write out the equation
[tex]x^2+6=-7x[/tex]Step 2: Rewrite the equation
[tex]x^2+7x+6=0[/tex]Step 3: Plot the graph of y = x² + 7x + 6
Step 4: Find the solution of the equation x² + 7x + 6 = 0
The solutions of x² + 7x + 6 = 0 are the x-coordinates of the points where the curve y = x² + 7x + 6 cuts the x-axis.
From the graph, we can see that the points are (-6, 0) and (-1, 0)
Hence, the solutions are -6, -1
Use a given information to create equation for the rational function. The function is written in factored form to help see how they given information shapes the equation. If the leading coefficient is not an integer enter the value as a fraction.
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Recall that a rational function:
[tex]\frac{P(x)}{Q(x)},[/tex]has a vertical asymptote at x₀ if and only if:
[tex]Q(x_0)=0.[/tex]Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:
[tex]Q(x)=x+1\text{.}[/tex]Since the rational function has a double zero at x=2 we get that its numerator must be of the form:
[tex]P(x)=k(x-2)(x-2)\text{.}[/tex]Finally, since the rational function has y-intercept at (0,2) we get that:
[tex]2=\frac{P(0)}{Q(0)}=\frac{k(0-2)(0-2)}{0+1}\text{.}[/tex]Simplifying the above equation we get:
[tex]\begin{gathered} \frac{k(-2)(-2)}{1}=2, \\ 4k=2. \end{gathered}[/tex]Dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4k}{4}=\frac{2}{4}, \\ k=\frac{1}{2}\text{.} \end{gathered}[/tex]Therefore, the rational function that satisfies the given conditions is:
[tex]f(x)=\frac{\frac{1}{2}(x-2)(x-2)}{x+1}\text{.}[/tex]Answer:
The numerator is:
[tex]\frac{1}{2}(x-2)(x-2)[/tex]The denominator is:
[tex](x+1)[/tex]What is the value of x please I need the answer ASAP !
Answers
Step 1
Since there are 3 equal sides in the diagram, the image redrawn will be
This is because both triangles are isosceles triangles and as such two sides are equal and the corresponding angles are also equal.
Step 2
The sum of angles in the quadrilateral will be 360°
Hence,
[tex]\begin{gathered} x+x+73+73+90=360 \\ \end{gathered}[/tex][tex]2x+146+90=360[/tex][tex]\begin{gathered} 2x=360-146-90 \\ 2x=\text{ 124} \\ \frac{2x}{2}=\frac{124}{2} \\ x=62^{\circ} \end{gathered}[/tex]Hence, x = 62°
Line HC is represented by the equation y=-x+4.1Determine the equation, in slope-intercept form, of theline DQ that is parallel to line HC and passes through thepoint D (1,0).y =
Answers
A linear equation has the general expression:
y=mx+b, where m is the slope of the line and b the intercept.
When two lines are parallel each other, this means that they have the same slope.
Line HC is represented by the formula: y=1*x+4, then it's slope equals 1, and it's intercept equals 4.
As mentioned, if line DQ is parallel to HC, then it's slope has to be equal to 1, let's write the formula of DQ with the information we have so far:
y=1*x+b,
Now, from the statement of the question, we know that line DQ goes through the point (1,0), which means that when x equals 1, y equals 0, let's replace this into the equation of line DQ and then solve for b.
y(1)=0=1*(1)+b, then:
b= -1
then the equation of line DQ is:
y=x-1, with an intercept of -1 and a slope of 1.
Describe the relationship between the two quantities.Volume of a cylinder; Height & radius of cylinder's base.inversejointdirectcompound
Answers
Answer:
Joint
Explanation:
[tex]\text{Volume of a cylinder}=\pi r^2h[/tex]The volume of the cylinder varies jointly with the radius, r and height, h.
The relationship is a joint variation.
10. Which function has the greatest value for x = 3?A. f(x) = 2 . 4xB. f(x) = 4 .22C. f(x) = 4 . x2D. f(x) = 2 x4
Answers
SOLUTION
We want to find the function that has the greatest value for x = 3
Note that the dot means multiplication
For A.
[tex]\begin{gathered} f\mleft(x\mright)=2\times4^x \\ f(3)=2\times4^3 \\ =128 \end{gathered}[/tex]For B
[tex]\begin{gathered} f(x)=4\times2^x \\ f(3)=4\times2^3 \\ =32 \end{gathered}[/tex]For C
[tex]\begin{gathered} f(x)=4\times x^2 \\ f(3)=4\times3^2 \\ =36 \end{gathered}[/tex]For D
[tex]\begin{gathered} f(x)=2\times x^4 \\ f(3)=2\times3^4 \\ =162 \end{gathered}[/tex]Hence the from our calculation, we can see that the answer is D. which is 162
Line f has a slope of -2/9. Line g is parallel to line f. what is the slope of line g?
Answers
If 2 lines are parallel, they both have the same slope.
So if line f has a slope of -2/9.
g (parallel) has a slope of -2/9
Question 10 of 10 Select the two values of x that are roots of this equation. x² + 2x - 4=0 . O A. x= -1- 5 B. X=-1+2.5 C. X=-1-2-15 D. X=-1+ 5 SUBMIT
Answers
Given
[tex]x^2+2x-4=0[/tex]Using the quadratic formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Given parameters} \\ a=1 \\ b=2 \\ c=-4 \end{gathered}[/tex]Subsitute the given parameters into the formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ x=\frac{-2\pm\sqrt[]{2^2^{}-4\times1\times-4}}{2\times1} \\ \\ x=\frac{-2\pm\sqrt[]{2^2+16}}{2} \\ \\ x=\frac{-2\pm\sqrt[]{4^{}+16}}{2} \\ x=\frac{-2\pm\sqrt[]{20}}{2} \\ \\ x=\frac{-2\pm\sqrt[]{4\times5}}{2} \\ x=\frac{-2\pm2\sqrt[]{5}}{2} \\ x=-1\pm\sqrt[]{5} \end{gathered}[/tex]The final answer
Option A and Option D
[tex]\begin{gathered} x=-1-\sqrt[]{5} \\ \text{and} \\ x=-1+\sqrt[]{5} \end{gathered}[/tex]The summary
write the equation in point slope and slope intercept form of a line that passes through the given point (-3, -4), and has the given slope m = -1/2
Answers
Question 1.
Given the point:
(-3, -4)
Slope, m = - 1/2
Let's write the equation of the line that passes through the given point with the slope in point-slope form and slope intercept form.
• Point slope form:
Apply the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Now substitute -1/2 for m, then input (-3, -4) for x1 and y1 in the equation above.
[tex]\begin{gathered} y-(-4)=-\frac{1}{2}(x-(-3)) \\ \\ y+4=-\frac{1}{2}(x+3) \end{gathered}[/tex]Therefore, the equation in point slope form is:
[tex]y+4=-\frac{1}{2}(x+3)[/tex]• SLope intercept form:
Apply the slope intercept form of a linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Substitute the following:
-1/2 for m
(-3, -4) for (x, y)
Then solve for b.
[tex]\begin{gathered} -4=-\frac{1}{2}(-3)+b \\ \\ -4=\frac{3}{2}+b \\ \\ \end{gathered}[/tex]Subtract 3/2 from both sides:
[tex]\begin{gathered} -4-\frac{3}{2}=\frac{3}{2}-\frac{3}{2}+b \\ \\ -\frac{4}{1}-\frac{3}{2}=b \\ \\ \frac{-8-3}{2}=b \\ \\ -\frac{11}{2}=b \\ \\ b=-\frac{11}{2} \end{gathered}[/tex]Therefore, the slope intercept form of the line is:
[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]ANSWER:
Point-slope form:
[tex]y+4=-\frac{1}{2}(x+3)[/tex]Slope intercept form:
[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]
I dont understand how to simplify an expression with exponents
Answers
Answer:
3^4
Step-by-step explanation:
Simplifying an expression with expression with exponents:
If they are dividing, we keep the base and subtract the exponents. For example:
[tex]\frac{a^x}{a^y}=a^{x-y}[/tex]In this question:
[tex]\frac{3^2}{3^{-2}}=3^{2-(-2)}=3^{2+2}=3^4[/tex]What is the best description for a trapizorid?A quadrilateral with just 1 pair of parallel sidesA parallelogram that can have 2 angles of equal measure A quadrilateral with no angles of equal measure a parallelogram with no sides of equal length
Answers
The best description is;
A quadrilateral with just 1 pair of parallel sides
Here, we want to selcect the best description that matches a trapezoid
A trapezoid is a four sided shape with two 2 parallel bases
A trapezoid can be isosceles, meaning that its side lengths might be equal
Hence, if two of the sides are equal, we can have that there are equal angles
Hence, the best description is a quadilateral with just a pair of parallel sides
Volume of a Cylinderarh.The volume of a cylinder with radius r and height h is given by the formula V =Find the volume of a cylinder with radius 9 cm and height 6 cm.cm3Round your answer to the nearest tenth if necessary.
Answers
Given
radius = 9 cm
height = 6 cm
Substitute the following to the formula for determining the volume of a cylinder.
r = 9, h = 6
[tex]\begin{gathered} V=\pi r^2h \\ V=(3.14)(9\text{ cm})^2(6\text{ cm}) \\ V=(3.14)(81\text{ cm}^2)(6\text{ cm}) \\ V=1526.04\text{ cm}^3 \end{gathered}[/tex]Rounding our answer to the nearest tenth, the volume of the cylinder is 1526.0 cubic centimeters.
Find the volume of the triangular prismn below.7 pt4 pt4 pt3.5 ft.4 ptO 47O 48O 49O 50
Answers
Answer
Option C is correct.
Volume of the triangular prism = 49 ft³
Explanation
The volume of any prism is given as
Volume of the prism
= (Area of the base or face that is seperated by a perpendicular distance) × (Perpendicular distance between the faces)
For this triangular prism, the base or face is a triangle.
Area of the base or face that is seperated by a perpendicular distance
= Area of a triangle
= ½ (Base) (Height)
= ½ (4) (3.5)
= 7 ft²
Perpendicular distance between the faces = 7 ft
Volume of the prism
= (Area of the base or face that is seperated by a perpendicular distance) × (Perpendicular distance between the faces)
= 7 × 7
= 49 ft³
Hope this Helps!!!
9/10-(1/5+1/2) what is the value of the expression?
Answers
start solving the sum of fractions that is inside the parentheses
[tex]\begin{gathered} \frac{9}{10}-(\frac{1\cdot2+5\cdot1}{5\cdot2}) \\ \frac{9}{10}-\frac{2+5}{10} \\ \frac{9}{10}-\frac{7}{10} \end{gathered}[/tex]then, solve subtraction of fractions with a common denominator
[tex]\begin{gathered} \frac{9-7}{10} \\ \frac{2}{10} \end{gathered}[/tex]simplify
[tex]\frac{2}{10}=\frac{1}{5}[/tex]Y varies directly with x. y=24 when x=6. Find y when x=8.
Answers
Answer:
Y varies directly with x.
This can be represented below as
[tex]\begin{gathered} y\propto x \\ y=kx \end{gathered}[/tex]Substitute the value of y=24 and x=6 to find the value of k
[tex]\begin{gathered} y=kx \\ 24=6k \\ divide\text{ both sides by 6} \\ \frac{6k}{6}=\frac{24}{6} \\ k=4 \end{gathered}[/tex]Substitute k=4 to get the equation connecting y and x
[tex]\begin{gathered} y=kx \\ y=4x \end{gathered}[/tex]Substitute the value of x=8 to get the value of y
[tex]\begin{gathered} y=4x \\ y=4\times8 \\ y=32 \end{gathered}[/tex]Hence,
The value of y when x= 8 is
[tex]\Rightarrow y=32[/tex]The 31st term of an arithmetic sequence is 496. If the common difference is 16, what is the second term?
Answers
Take into account that the general expression for the nth term of a arithmetic sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]where, for this case:
an: 31st term = 496
n = 31
d: common difference of the sequence = 16
a1 = first term = ?
Solve the previous equation for a1, replace the values of the parameters and simplify:
[tex]\begin{gathered} a_1=a_{31}-(31-1)16 \\ a_1=496-(31)16 \\ a_1=0 \end{gathered}[/tex]Then, the nth term can be written as follow:
[tex]a_n=(n-1)d[/tex]and the second term is given by (n = 2):
[tex]a_2=(2-1)16=16[/tex]Hence, the second term is 16
What congruence rule does this follow? What is the congruence statement? congruence statement: triangle ABC is congruent to triangle _______
Answers
Given data:
The given figure.
In triangle ABC and triangle CDB.
[tex]\begin{gathered} AB=CD \\ AC=BD \\ BC=BC \end{gathered}[/tex]Thus, the triangle ABC is congruent to the triangle CDB by side-side-side rule.
Darrin needs to calculate the length of the sides of water tank that will be in shape of a cube. The tank must hold 343 cubic meters of water . How long should the sides be
Answers
According to the information given in the exercise:
- The water tank will be in the shape of a cube.
- It must hold this volume of water:
[tex]V=343^{}m^3[/tex]In order to solve the exercise, you need to remember the formula for calculating the volume of a cube:
[tex]V=a^3[/tex]Where "a" is the length of any edge of the cube.
In this case, knowing the volume of the tank, you can substitute it into the formula and solve for "a", in order to find the length of its sides. Then, you get:
[tex]\begin{gathered} 343^{}m^3=a^3 \\ \\ \sqrt[3]{343^{}m^3}=a \\ \\ a=7m \end{gathered}[/tex]Hence, the answer is:
[tex]7\text{ }meters[/tex]Which ratios form a proportion2/3 and 8/12. 3/4 and 9/16. 1/6 and 3/8. 2/5 and 5/2
Answers
proportions means having equal amounts of something when shared
the first ratio are
2/3 and 8/12
equating the two expressions
2/3 = 8/12
introducing cross multiplication
2 x 12 = 3 x 8
24 = 24
this form a proportion coz the left hand side is equal to the right hand side
the second question
3/4 = 9/16
cross multiply
3 x 16 = 4 x 9
48 = 36
48 is not equal to 36, therefore this cannot form a proportion
If one of the 50 states is chosen at random, then a standard die is rolled, Find the probability of getting a state that starts with the letter N, then a number that is at least 2.
Answers
We have that the US states that start with the letter 'N' are:
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
The probability of selecting a state that starts with an N is 8/50, and the probability of rolling at least a 2 in a die is 5/6, therefore:
[tex]\begin{gathered} P(\text{select state that starts with an N and rolling at least a 2)=} \\ (\frac{8}{50})(\frac{5}{6})=\frac{40}{50\cdot6}=\frac{40}{300}=\frac{4}{30}=\frac{2}{15} \end{gathered}[/tex]therefore, the probability is 2/15
A veterinarian measured the weights ofthree kittens on a scale. She recorded theweights in the table below.
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Total weight of the kittens = 2.8 lbs + 3.2 lbs + 4.0lbs= 10lbs
Percentage of kitten C is given as
[tex]\begin{gathered} \frac{4}{10}\text{ x 100} \\ =\text{ 40\%} \end{gathered}[/tex]Mrs. jones has 4 dogs. she has 8 1/6 pounds of food left. if each dog eats an equal amount of the food, how much food will each dog eat? what is the equation.
Answers
Given that Mrs Jones has 4 dogs and she has 8 1/6 pounds of food.
Let x represent the amount of food each dog will eat.
Then it can be represented by the equation;
[tex]4x=8\frac{1}{6}[/tex]to solve for x, let us divide both sides by 4;
[tex]\begin{gathered} \frac{4x}{4}=\frac{8\frac{1}{6}}{4} \\ x=2\frac{1}{24} \end{gathered}[/tex]Therefore, the amount of food each dog will eat is;
[tex]2\frac{1}{24}\text{ pounds}[/tex]
Divide g(x) = x^4 - 2x^3 + X + 3 by x+3
Answers
Let's first get the coefficients of the numerator: x^4 - 2x^3 + x + 3 = 1, -2, 0, 1, 3
There is no x^2 in the expression, thus, the coefficient for x^2 = 0
Zero of the denominator: x + 3; x = -3
Using synthetic division,
-3 I 1 -2 0 1 3
I_________________
-3 I 1 -2 0 1 3
I_________________
1
-3 I 1 -2 0 1 3
I_____-3___________
1 -5
-3 I 1 -2 0 1 3
I_____-3__15_______
1 -5 15
-3 I 1 -2 0 1 3
I_____-3__15_-45____
1 -5 15 -44
-3 I 1 -2 0 1 3
I_____-3__15_-45____
1 -5 15 -44
-3 I 1 -2 0 1 3
I_____-3__15_-45_132__
1 -5 15 -44 135
The remainder is 135. Which transforms it into 135/x+3.
Thus, the quotient of x^4 - 2x^3 + x + 3 divided by x + 3 is:
[tex]x-5x^2+15x\text{ - 44 + }\frac{135}{x+3}[/tex]hello am trying to make sure I did this right
Answers
A.
The rate of change is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]using the origin (0,0) and the point (4,60) on the graph we have:
[tex]m=\frac{60-0}{4-0}=\frac{60}{4}=15[/tex]Therefore the rate of change is 15.
B.
The equation of a line is given by:
[tex]y=mx+b[/tex]where m is the rate of change and b is the y-intercept. In this case we know that the rate of change is 15 and we also know that she started her dide 120 km from the ending point. From the graph this means that the y intercept is zero, then the equation is:
[tex]y=15x[/tex]Show the numbers on the place value chart. Use >, <, or = to compare.167.4167.462r notes
Answers
Given:
[tex]167.4\text{ \& }167.462[/tex][tex]167.4<167.462[/tex]Is the function represented by the table linear?ху-6101111261312Yes, because it has a constant rate of change.O Yes, because it does not have a constant rate of change.No, because it has a constant rate of change.O No, because it does not have a constant rate of change.
Answers
ANSWER
Yes, because it has a constant rate of change.
EXPLANATION
We want to check if the function represented in the table is a linear function.
A linear function is one in which there are two variables that are related in such a way that a change (increase or decrease) in one variable (independent variable) leads to a proportional change (increase or decrease) in the second variable (dependent variable).
If we look at the two variables given in the table, we see that as the x variable increases, there is a proportional increase in the y variable.
So we can say that there is a constant rate of change.
So, we can conclude that it is a Linear Function.