[tex]\dfrac{z}{10} =5[/tex]
Multiply both sides by 10:
[tex](\dfrac{z}{10} )\times10=(5)\times10[/tex]
[tex]\fbox{z = 50}[/tex]
z/10 = 5
Multiply both sides by 10:
z/10 * 10 = 5 * 10
z = 50
! the lengths of the sides of a triangle are 8, 8, and 3. what is the measure of the smallest angle in the triangle?
and how did we find it ?
The measure of the smallest angle in the triangle is 10.8°
What is an isosceles triangle?An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.
The corresponding angles of the two equal lengths in an isosceles triangle are equal. This means that if we represent the two angles by x and the the third angle by y , then 2x+y = 180.
using cosine rule c² = a²+b²+2abcosC
a = 8, b = 8 and c = 3
3² = 8²+8²+2×8×8cos C
9 = 64+64+128cos C
128cosC = 9- 128
cos C = -119/128
cos C = -0.93
C = cos^-1 0.93
C = 158.4°
therefore 158.4 + A+ B = 180
A= B
2A = 180-158.4
2A = 21.6
A = 21.6/2
A = 10.8°
therefore A = B = 10.8°. This means the value of the smallest angle is 10.8°
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4) Evelyn used the proportion y/x = 5/3
when deriving the equation of a line with similar triangles. Which of these statements about the line are correct? Select two.
Using the slope-intercept form of the equation of a line, the correct statement are:
The slope of the line is 5/3
The y-intercept of the line is 0
Slope-intercept form of the equation of a lineFrom the question, we are to determine the statements about the given line that are correct
The given equation is
y/x = 5/3
To determine the statements that are correct, we will write the equation of the line the slope-intercept form of a line
The slope-intercept form of a line is given by
y = mx + b
Where m is the slope
and b is the y-intercept
Writing the equation in the slope-intercept form
y/x = 5/3
y = 5/3(x)
By comparing with the slope-intercept form of a line,
m = 5/3
c = 0
Thus,
The slope is 5/3
and the y-intercept is 0
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Write an equation in slope intercept from that describes the data in the table. X -2, 1, 4, 6, 12 and y -6, -1.5, 3, 6, 13.5
Answer:
multiply
(x square + 5) ( x square +2x - 3)
help pls I am stuck math is over my head
Answer:
6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?
B. Z is divisible by X7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?
B. He stopped at a place in between for 50 seconds,8. How many TENS must be added to 7 000 to make it 70 000.
(70 000 - 7 000) / 10 = 6 300C. 6 300Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-what level of correlation between two independent variables in a regression model generally will cause multicollinearity problems.
The two levels of correlation coefficients are as follows:
A correlation coefficient less than -0.7.
A correlation coefficient greater than +0.7.
A correlation coefficient is a statistical degree of the diploma to which modifications to the fee of 1 variable expect alternate to the fee of another. In definitely correlated variables, the fee will increase or decreases in tandem.
The two levels of correlation coefficients are as follows:
A correlation coefficient less than -0.7.
A correlation coefficient greater than +0.7.
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PLEASE HELP ASAP!!!!!!!
1) If the slope of line a is 5 and the slope of line b is -5, then what is true about lines a and b (assume lines a and b are coplanar)?
A. they are parallel
B. they are perpendicular
C. they are intersecting lines
2) If the slope of line a is 1/4 and the slope of line b is -1/4, then what is true about lines a and b (assume lines a and b are coplanar)?
A. they are parallel
B. they are perpendicular
C. they are intersecting lines
3) If the slope of line a is 3 and the slope of line b is 3, then what is true about lines a and b (assume lines a and b are coplanar)?
A. they are parallel
B. they are perpendicular
C. they are intersecting lines
On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines
what are perpendicular lines?A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.
1) For this case, we have to define perpendicular lines:
[tex]m1 * m2 = -1[/tex]
[tex]m1 = 1/5\\m2 = -5\\so, m1*m2 = -1\\[/tex]
they are perpendicular
2) they are perpendicular
3) they are intersecting lines
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today b is 3 times older than a. in 5 years b will be 2 times older than a. how old are a and b today?
If we substitute a = 5 into the equation 3a = 15, we get b = 15.
Therefore, a = 5 and b = 15.
We are given that b is 3 times older than a, so b = 3a.
We are also told that in 5 years b will be 2 times older than a, so b = 2(a + 5).
We can set 3a = 2(a + 5) and solve for a.
3a = 2a + 10
2a = 10
a = 5
Therefore, a = 5 and b = 3a = 15.
We know that today, b is 3 times older than a. This means that b = 3a. We can use this equation to help us solve the problem.
We know that in 5 years' time, b will be 2 times older than a. This means that in 5 years, b = 2(a + 5). We can use this equation to help us solve for a and b.
We can set the two equations equal to each other, 3a = 2(a + 5). We can then solve for a, which gives us a = 5.
We can then substitute this value into either of the equations to find the value of b. If we substitute a = 5 into the equation 3a = 15, we get b = 15.
Therefore, a = 5 and b = 15.
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someone answer what pair of transformations is equivelent to the transformation described by (xx,y) -(x,-y+1)?
The pair of transformations that is equivalent to the transformation described by (x,y) -> (x,-y+1) is (x, -y) and (x, y + 1)
How to determine the pair of transformations?From the question, we have the following parameters that can be used in our computation:
(x,y) ⇒ (x,-y+1)
The above represents the transformation from a point to the image of the point
The first transformation is from
(x,y) ⇒ (x,-y)
This represents a reflection across the x-axis
The second transformation is from
(x,-y) ⇒ (x,-y + 1)
This represents a translation up by 1 unit
Hence, the pair of transformations is (x,y) ⇒ (x,-y) and (x,-y) ⇒ (x,-y + 1)
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Which histogram depicts higher standard deviation? L Choose the correct answer below Histogram depicts the higher standard deviation, because the distribution has more dispersion Histogram depicts the higher standard deviation, because the bars are higher than the average bar in b Histogram depicts the higher standard deviation since is more bell shaped_ D. Histogram depicts the higher standard deviation because the distribution has more dispersion
The histogram that depicts the higher standard deviation is the one that has a wider spread of data, meaning the distribution has more dispersion.
This can be seen by the points in the histogram being more spread out and having a larger range of values. The bars may be higher than the average bar in b, but that does not necessarily mean it has a higher standard deviation. Similarly, a more bell-shaped distribution does not necessarily indicate a higher standard deviation.The histogram that depicts the higher standard deviation is the one that has a wider spread of data, meaning the distribution has more dispersion. This is because a higher standard deviation indicates that the data points are more spread out, and the range of values is larger. This can be seen by looking at the histogram and observing that the points are more spread out and have a larger range of values. The bars in the graph may be higher than the average bar in b, but this does not necessarily mean that it has a higher standard deviation. Similarly, a more bell-shaped distribution does not necessarily indicate a higher standard deviation.
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A line passes through the points (4, - 3) and (6, - 1) The equation of the line in slope -intercept form is y = mx + b . What is the value of b?
Answer:
-7
Step-by-step explanation:
First find the slope (m)
m = (-1-(-3) / (6-4) = 2/2 = 1
Now find b, the y-intercept, by plugging either point into the equation.
y = mx + b
-3 = 1(4) + b
b = -7
Line segment su is dilated to create s'u' using point q as the center of dilation. the scale factor of the dilation is
The scale factor of the dilation is 2 which can be shown in the details given below.
In geometry, a line segment is bounded with the aid of using awesome factors on a line. Or we are able to say a line phase is a part of the road that connects factors. A line has no endpoints and extends infinitely in each the course however a line phase has constant or particular endpoints.
QS : QS'
= 4 : 8
= QU : QU'
= 5 : 10
= 1 : 2
Then the scale factor is of the dilation is 2 (magnification).
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Complete question
Line segment SU is dilated to create S'U' using point Q as the center of dilation.
The scale factor of the dilation is:
Help pls I don’t understand
Answer: I think its
x>-10/3
Step-by-step explanation:
The cost of 7 sandwiches and 5 milkshakes is $79. The cost of 2 sandwiches and 5 milkshakes is $44. How much does one sandwich cost and one milkshake cost?
HELP
Cost of one sandwich is $7 and cost of milkshake $5.
What is an equation?
In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
According to question:
let cost of one sandwich be x and cost of milkshake be y .
7x + 5y = $79 -------(1)
2x + 5y = $44 -------(2)
subtracting equation 2 from 1 , we get
5x = 35
x = $7
so cost of one sandwich is $7.
now substituting value of x in equation 1 , we get
7(7) + 5y = 79
49 +5y = 79
5 y = 20
y = 4
so cost of one milkshake is $5.
Hence cost of one sandwich is $7 and cost of milkshake $5.
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7/4 of a number is 66 what is the number
Answer:
7x/4 = 66
(7/4)x = 66
x = 66 × (4/7)
x = 264/7
in decimal x = 37.714(apprx.)
The equation f(t) = 24,500 x (0.88)t represents the value of a car, in dollars, years after it was purchased.
What do the numbers 24,500 and 0.88 mean?
What does represent?
Sketch a graph that represents the function and shows and .
the function should be represented as f(t) = 24,500( 0.88[tex])^{t}[/tex]
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Given, f(t) = 24,500 x (0.88)t
Assuming that the value of the car only increases by 88% per year compared to the previous year, the function rule needs to have "t" as the exponent, thus it should be f(t) = 24,500( 0.88[tex])^{t}[/tex]
Hence, the function should be represented as f(t) = 24,500( 0.88[tex])^{t}[/tex]
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ga rectangular enclosure at a zoo is 35 feet long by 18 feet wide. the zoo doubles the area of the enclosure by adding the same distance to the length and width. what are the new dimensions of the enclosure?
The new length is 35+10=45 and the new width is 18+10=28.
To Find the Area of a rectangle is length times the width.
Given that enclosure at the zoo is 35 feet long by 18 feet wide. It means the length is 35 feet and the width is 18 feet.
Area of Rectangle=Length × Width
=35×18
=630
The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.
(35+x)×(18+x)=1260
630+35x+18x+x2=1260
x2+53x+630-1260=0
x2+53x-630
Now we will apply the quadratic formula we get
x=10.
The new length is 35+10=45
The new width is 18+10=28.
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Anna is knitting hats to give as gifts. Each one will use 1. 2 skeins, and she has 6 skeins of yarn available. With the yarn available, how many hats can anna knit?.
An equation which suggests how the range of skeins of yarn remaining, y, relies upon at the range of hats Anna knits, x is y =6- 1.2x.
An expression is a mathematical equation that is used to reveal the connection present among or extra variables and numerical quantities.
Let y constitute the range of skeins of yarn remaining. Let x constitute the range of hats Anna knits.
Mathematically, an equation which fashions the connection among x and y is given by: Mathematically, an equation which fashions the connection among x and y is given by
Remaining yarn = Total quantity of yarns -
Number of yarns used in keeping with hats
Substituting the given parameters into the formula, we have;
y = 6 - 1.2x
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Oscar is 12 years old and his little sister is 6. Oscar uses a to represent his age. He says that he can use the expression a = 2 to always know his sister's age. Do you agree? Explain.
Oscar's statement that he can use the expression a = 2 to always know his sister's age is false
How to determine the true statement?From the question, we have the following parameters that can be used in our computation:
Oscar = 12
His sister = 6
Equation: a = 2x
Where x = his sister's age
The above equation means that
He is always twice as old as his sister
This statement is false, because the equation is only true when he is twelve
When he is 13, his sister will be 7
And a =2x, will be false
Hence. Oscar's statement is false
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this table shows the input and output values for an exponential function f(x). what is the ratio of outputs for any two inputs that are one value apart? responses 18 one eighth 12 one half 4 4 2
The question asks for the multiplicative rate of change which has a formula:[ f(x2) / f(x1) ] / (x2 - x1). The answer is 2.
How do you find the multiplicative rate of change?If we want to find the multiplication. Tive rate of change of a function, that just means we need to divide one item by the one that comes before it to find out how much it multiplies Given one change in acts.
A ratio is a divisional comparison of two numbers by dividing the second output by the first one and using the first two outputs, -1/8 and -1/4, we can determine the ratio:
-1/4 ÷ -1/8
When dividing fractions, we multiply by the reciprocal:
-1/4 × -8/1
To multiply fractions, multiply straight across:
(-×-8)/(4×1) = 8/4 = 2.
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scores on an english test are normally distributed with a mean of 30.6 and a standard deviation of 6. a) what percentage of students score below 33? b) find the score that is at the 80th percentile.
(a) 0.65542 proportion of pupils receive a score below 33.
b) the score that falls within the 80% range is 35.64.
Given that,
English test results have a mean of 30.6 and a standard deviation of 6, and they are normally distributed.
We have to find
(a) What proportion of pupils receive a score below 33.
b) Determine the score that falls within the 80% range.
We know that,
X: Scores of an english test
X≈N(30.6 , 6²)
(a) P(X<33)= P(Z<33-30.6/6)
=P(Z<0.4)
=1-P(Z>0.4)
=1-0.34458
=0.65542
(b) P(X<x)=0.80
P(Z<x-30.6/6)=0.80
1-P(Z>x-30.6/6)=1-0.80
P(Z>x-30.6/6)=0.20
x-30.6/6=0.20
x= 35.64
Therefore,
(a) 0.65542 proportion of pupils receive a score below 33.
b) the score that falls within the 80% range is 35.64.
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given a rectangular sheet of cardboard 16 inches by 10 inches youa re asked to cut off identical squares from each of the four corners of the sheet and then bend up the sides of the remaining cardboard to form a rectangular box. what is the maximum volume of the box
If the dimensions of the cardboard sheet is 16 inches by 10 inches , then the maximum volume of the box is 144 in³ .
In the question ,
it is given that the length of the sheet is = 16 inch
and width of the sheet is = 10 inch
let width of box be ⇒ "w" ,
let length of box be ⇒ "l"
let the length of the corner cut out be = "x"
let volume of box be ⇒ "V" ;
we need to find the point of dV/dx that is maximum ,
given width = 16 ; and length = 10 ,
we have : width = x + w + x ⇒ w = 2(8 - x)
length = x + l + x = 10 ⇒ l = 2(5 - x)
the Volume of rectangular box is written as ; V = w*l*x ;
substituting the values of w , l and x ,
we get ;
V = 2(8 - x)2(5 - x)x
V = 4x³ - 52x² + 160x
differentiating with respect to "x" , and for critical point equating it to 0 ,
we have ;
12x² - 104x + 160 = 0
solving the above quadratic, we get ;
x = 2 & x = 20/3 .
On substituting the values , in d²V/dx² = 24x - 104 < 0 for x = 2 ,
that is maximum ;
Substituting x = 2 , in the V = 4x³ - 52x² + 160x ,
we get ;
Volume of the box as 144 in³ .
Therefore , the maximum volume of the box is = 144 in³ .
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Answer:
d
Step-by-step explanation:
d
Graph the inequality 7≤ y -3x<11
The graph of inequality 7 ≤ y - 3x < 11 is attached below.
What is inequality?Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal.
Given:
The inequality = 7≤ y -3x < 11
Therefore, the graph of inequality 7 ≤ y - 3x < 11 is attached below.
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Solving linear systems with 3 variables
Solve for x y and z using substitution
5x+2y-2z=-57
3x-10y-z=-11
y=-2
Answer:
x=-9
y=-2
z=4
Step-by-step explanation:
5x+2y-2z=-57
3x-10y-z=-11
y=-2
5x+2(-2)-2z=-57
3x-10(-2)-z=-11
y = -2
5x-4-2z=-57
3x+20-z=-11
y = -2
5x-2z=-53
3x-z=-31
y = -2
5x-2z=-53
3x+31=z
y = -2
5x-2(3x+31)=-53
3x+31=z
y = -2
5x-6x-64=-53
3x+31=z
y = -2
-x=9
3x+31=z
y = -2
x=-9
3(-9)+31=z
y = -2
x=-9
-27+31=z
y = -2
x=-9
z=4
y = -2
A diver is at a certain depth in the ocean. After ascending 10 3/4 feet, the diver is now at a depth of -56 1/2 feet, Write and solve an equation to determine the diver’s initial depth.
Equation to determine the diver’s initial depth is [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable.
The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.
Let the distance of diver at a certain depth be x.
After some time he ascends [tex]10\frac{3}{4}[/tex] feet.
The final position of diver is : [tex]56\frac{1}{2}[/tex] feet.
Using given information we get the required equation: [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].
where x = distance of diver at a certain depth.
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20 Emily wants to insert nine numbers into the 3 x 3 table so that the sum of the numbers in two adjacent cells (with a common side) is always the same. She has already written two numbers into the table. How big is the sum of all nine numbers? 8 (0) (D) 22 (B) 20 (C) 21 (0) 19 (E) 23
Answer:
D) 22
i hope it's correct
The requried sum of all nine numbers would be equal to 22. Option B is correct.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
For 3 x 3 tables,
Emily already wrote two numbers one is 2 in the 1 cell of the table and 3 in the 6th cell of the table.
For the given conditions for each side of cells in the table, the sum of the two adjacent cells must be equal.
So, If two is located at 1st cell, we put 3 on both the adjacent sides of 2 and 2 on both adjacent sides of 3 so that the sum equal to 5,
And the whole 3x3 table is given as,
2 3 2
3 2 3
2 3 2
Now, sum of all the digits, = 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 = 22
Thus, the requried sum of all nine numbers would be equal to 22. Option B is correct.
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Which is greater 30% of 105 or 32% 98
Answer: 30% of 105 (= 31.5)
Step-by-step explanation:
30% of 105 is 31.5 and
32% of 98 is 31.36
Show all steps necessary to verify the trigonometric identity: 1+tan^2x/tan^2x=csc^2x
The values represent a direct variation. Indentify the constant and find the missing value.
K=xy
The required missing value for the values representing the direct variation is -3.2.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
let the missing number be x.
From the table given,
-22/-4.4 = -16 / x
x = -16 / 5
x = -3.2
Thus, the required missing value for the values representing the direct variation is -3.2.
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Trigonometry I need help
3) The value of x is 40°.
4) The value of x is 54.67°.
5) The value of x is 11.15.
6) The value of x is 30.33.
What is sine of an angle?
Sine and cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as the ratio of the length of the side directly opposite the angle to the length of the longest side of the triangle (the hypotenuse), and the neighboring leg's length to the hypotenuse, respectively. The sine and cosine functions are abbreviated sin and cos for an angle theta.
3)
The height of the triangle is 9.
The hypotenuse of the angle is 14.
The angle between base and hypotenuse is x°.
sin θ = height/hypotenuse
Putting θ = x°, height = 9 and hypotenuse = 14:
sin x = 9/14
x = 40°.
4)
The height of the triangle is 31.
The hypotenuse of the angle is 38.
The angle between base and hypotenuse is x°.
sin θ = height/hypotenuse
Putting θ = x°, height = 31 and hypotenuse = 38:
sin x = 31/38
x = 54.67°.
5)
The height of the triangle is x.
The hypotenuse of the angle is 17.
The angle between base and hypotenuse is 41°.
sin θ = height/hypotenuse
Putting θ = 41°, height = x and hypotenuse = 17:
sin 41 = x/17
x = 17 × sin 41
x = 11.15.
6)
The height of the triangle is 29.
The hypotenuse of the angle is x.
The angle between base and hypotenuse is 73°.
sin θ = height/hypotenuse
Putting θ = 73°, height = x and hypotenuse = 17:
sin 73 = 29/x
x = 29 / sin 73
x = 32.33
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What is the equation of the vertical line through (-5,-2)(−5,−2)left parenthesis, minus, 5, comma, minus, 2, right parenthesis?
Answer:
x=- 5
Step-by-step explanation:
A vertical line has an undefined slope (the rise is divided by zero, since there is no change in x. x is always -5.
The required equation of the vertical line will be x = -5 which passes through the points (-5,-2).
What is the vertical line?The equation of a vertical line is of the form x = k, where k is the x-coordinate of the point through which the line passes.
The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
We know that a vertical line's equation is x = k, where k is the x-coordinate of the point at which the line crosses.
As per the given question, the line passes through the point (-5, -2), so the equation of the line is x = -5.
A vertical line has an undefined slope (since there is no change in x, the rise is divided by zero). x is always a negative five number.
Therefore, the required equation of the vertical line will be x = -5.
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