8x+30=110
8x=110-30
8x=80
x=80/8
x=10
I need help please, Consider triangle ABC. Determine whether each statement is true of false.
HELPPP it’s a test quest.. 30pts
Answer:
Should be the first one. You have $5 flat fee and an additional 10 cents per text. Then you have a $10 flat fee and an additional 5 cents per text. so the first equation would be 0.1x + 5 and the second one would be 0.05x + 10
What is the distance between the points
(-7,1) and (-7,-5) on the coordinate
plane?
The distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.
The distance formula is a useful tool in many areas of mathematics and science, such as geometry, physics, and engineering. It can be used to find the distance between two points in any number of dimensions, not just two dimensions as in the coordinate plane In addition, the distance formula can also be used to find the length of a line segment in the coordinate plane, which is just the distance between its endpoints. This can be useful in finding the shortest distance between two points, or in finding the length of a path that connects two points.
The distance formula is a mathematical equation used to find the distance between two points in the coordinate plane. It makes use of the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In the coordinate plane, we can represent each point by its coordinates (x1, y1) and (x2, y2). The distance between the points is then given by the equation:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For the points (-7,1) and (-7,-5), we can plug in the values into the equation:
distance = sqrt((-7-(-7))^2 + (-5-1)^2) = sqrt(0^2 + (-6)^2) = sqrt(36) = 6
So the distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.
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HELPPPP ASAPP WILL MARK BRAINLIST
Which sequence of transformation results and figures that are similar, but not congruent?
A. Reflected across the X axis, then dilated by a factor of 1/3
B. Rotated counterclockwise 90° then translated six units to the left
C. Translated to units down, then reflected across the Y axis
D. Reflected across the Y axis then translated seven units to the left
Help help me plsssssSss
Answer:
Step-by-step explanation:
it is that because it equalls with positives numbers and if u do your calculation maybe youll undestand
-10(1 - 9x) + 6(x - 10)
Pics pls
Answer:
\(\boxed{\sf{96x-70}}}\)Step-by-step explanation:
Use the distributive property.
What is a distributive property?Distributive property is a serving to distribute or allot or disperse.
Distributive property:
A(B+C)=AB+AC
A(B-C)=AB-AC
-10(1-9x)+6(x-10)
Expand.
-10(1-9x)
-10*1=-10
-10*9x=90x
\(\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}\)
6(x-10)
6*x=6x
6*10=60
6x-60
Rewrite the problem down.
= -10+90x+6x-60
Combine like terms.
90x+6x-10-60
Add the numbers from left to right.
90x+6x=96x
96x-10-60
Finally, subtract the numbers from left to right.
-10-60=-70
\(\Longrightarrow \boxed{\sf{96x-70}}\)
Therefore, the final answer is 96x-70.
I hope this helps, let me know if you have any questions.
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Distributive Property :
\(-10(1-9x)+6(x - 10)\)
\(-10(-9x+1)+6(x - 10)\)
\(90x-10+6x-60\)
\(90x-70+6x\)
\(96x-70\)
\(answer : \boxed{\pink\star\tt{96x-70}}\)
━━━━━━━━━━━━━━━━━━━━━━━━
Common factor :
\(- 10(1 - 9x) + 6(x - 10)\)
\(96x - 70\)
\(2(48x - 35)\)
\( answer : \boxed{ \pink \star\tt{2(48x - 35)}}\)
Let f (x) = −x2 −5x + 36. What is the value of f (−3)?
Answer:
Step-by-step explanation:
You just have to substitute -3 into your function.
Therefore: 9 + 15 + 36 = 50
The value of the f (−3) is 42 after plugging the value of x = -3 in the function f(x) = -x² - 5x + 36.
What is a function?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.
It is given that:
f(x) = -x² - 5x + 36
Any function of the form \(\rm f(x) =ax^2+bx+c\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
Plug x = -3 in the above function:
f(-3) = -(-3)² - 5(-3) + 36
f(-3) = -9 + 15 + 36
f(-3) = 42
Thus, the value of the f (−3) is 42 after plugging the value of x = -3 in the function f(x) = -x² - 5x + 36.
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I need help with this
a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).
To solve:
12 - 4x = 15 - 3x
12 = 15 + x
-3 = x
Therefore, x is equal to -3.
b) To find the value of AB, plug in the value of x found in part a).
12 - 4x
12 - 4(-3)
12 - (-12)
12 + 12 = 24
Thus, segment AB is equal to 24.
c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.
15 - 3x
15 - 3(-3)
15 - (-9)
15 + 9 = 24
Thus, segment DE is also equal to 24.
We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.
I hope this helps!
Choose the word that correctly completes the statement. Since angle B is the largest angle, is the ________ side. adjacent included longest shortest
Since angle B is the largest angle, Line segment A C is the longest side. option C
How to complete the statementTo complete the statement, we need to know that;
Using the sine rule of a triangle, we can know that the sin value of an angle will be directly related to the length of the side it's facing.
Angle B is the largest angle out of the three. The sin value of an angle will be larger if the angle is larger (from 0 to 90). Sin 75 is 0.97, sin 60 is 0.87, and sin 45 is 0.71
That means the largest angle will have the largest sin value. The largest sin value means the side will be the longest side.
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The complete question:
Choose the word that correctly completes the statement. Triangle A B C is shown. Angle A C B is 45 degrees, angle C B A is 75 degrees, and angle B A C is 60 degrees. Since angle B is the largest angle, Line segment A C is the ________ side.
adjacent
included
longest
shortest
can yall plz plz help me
Answer:
the answer is 80000 is b
Find the two errors and solve the problem correctly.
Draw a diagram to show the given information,
Given:
JE is the perpendicular bisector of DF,
H is the midpoint of Je.
His the midpoint of GI
The diagram to fix:
The two errors made are angle 90 was not indicated to be formed at the point of intersection of the bisector and also wrong indication of congruent segments.
The diagram has been fixed. See attachment below for the fixed diagram.
In order to understand the errors in the diagram, note the following:
A perpendicular bisector divides a line segment into two equal halves and also forms a right angle at the point of intersection.
Congruent segments are indicated by equal number of strokes. i.e. small straight lines to indicate congruency.
The TWO ERRORS:
1. There's no indication on the point of intersection that a right angle was formed on both sides of the segment bisected.
2. The equal segments are not well labelled or indicated. arEH and HJe indicated that they are equal using one stroke.
GH and HI is another set of congruent segments that should be indicated with different number of strokes to indicate only both of them are equal segments.
In summary, the two errors made are angle 90 was not indicated to be formed at the point of intersection of the bisector and also wrong indication of congruent segments.
The diagram has been fixed. See attachment below for the fixed diagram.
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Haley worked 297 hours during the summer and earned $11 for each hour she worked. Which is the best estimate for the total amount she earned?
A.
$3,000
B.
$2,000
C.
$1,500
D.
$4,000
A
hdhdusisjdjsjskkdjskwkkwosododo
bfbd
Answer:
its A
Step-by-step explanation:
suppose the proportion of students in school a diagnosed with adhd is p1 and the proportion of students in school b diagnosed with adhd is p2. state the null hypothesis for a test to determine if school a has the lower proportion of students diagnosed with adhd.
H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)
Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.
Symbolically, the null hypothesis can be stated as:
H0: p1 ≥ p2
Where:
H0: Null Hypothesis
p1: Proportion of students diagnosed with ADHD in School A
p2: Proportion of students diagnosed with ADHD in School B
In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.
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2 rulers cost 1.20 then how much does 6 ruler’s cost
Answer: 3.60$ it is very simple think about it
Answer:
3.60
Step-by-step explanation:
2 rulers = 1.20
2x3=6
so times 1.20 by 3 too
6 rulers = 3.60
Solve the equation for the variable.
\( \frac{2}{5} x + 15 = x - 6\)
x = [?]
Answer:
x = 35Step-by-step explanation:
\(\frac{2}{5} x + 15 = x - 6\)
First multiply through by 5 to eliminate the fraction
That's
\(5 \times \frac{2}{5} x + 15(5) = 5x - 30 \\ 2x + 75 = 5x - 30\)
Next using the subtraction property subtract 5x from both sides
That's
\(2x - 5x + 75 = 5x - 5x - 30 \\ - 3x + 75 = - 30\)
Next subtract 75 from both sides
\( - 3x + 75 - 75 = - 30 - 75 \\ - 3x = - 105\)
Divide both sides by - 3
\( \frac{ - 3x}{ - 3} = \frac{ - 105}{ - 3} \)
We have the final answer as
x = 35Hope this helps you
Question is in the image below
9514 1404 393
Answer:
A) r = d/t
B) 221,760 ft/h
C) 42 mi/h
D) miles; the number is more comprehensible
Step-by-step explanation:
A) Given d = rt
Divide by the coefficient of r to solve for r.
r = d/t
__
B) Fill in the given numbers to find the rate in ft/h.
r = (665,280 ft)/(3 h) = 221.760 ft/h
__
C) Multiply by the conversion factor (1 mi)/(5280 ft) to convert to miles.
(221,760 ft/h)(1 mi)/(5280 ft) = 42 mi/h
__
D) For this scenario, miles per hour is a better unit for speed. Many people have seen that speed registered on a speedometer, so have some sense of what it means. Often numbers outside the range of 1 to 1000 are beyond ready comprehension.
Solve the following linear system of equations by Cramer's rule method;
2x+4y+2z=16
−2x−3y+z=−5
2x+2y−3z=−3
Rearrange as the form of Ax=B
Find the inverse of the coefficient matrix (A⁻¹); and
Solve the system of equations
The solution of the given linear system of equations is x = 2, y = 1 and z = 2.
Given that the linear system of equations is
2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3
To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:
A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]
To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:
|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12
The determinant is non-zero, hence A is invertible
A⁻¹ = 1/|A| [adj A]
where adj A is the transpose of the cofactor matrix [C] of A:
adj A = [C]T
So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:
C = [5, 2, 6; 2, -2, 2; -4, -4, -4]
Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]
To solve the system of equations, we have x = A⁻¹B as below:
x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]
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There are 25 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in
the dance recital?
There are
Imen in the dance recital.
If the ratio is 2:5 when there are more females then men 25 divided by 5 is 5 and 2 multiplied by 5 is 10.
So to answer your question: There are 10 Men
as the spacing between joists increases, the maximum span for any board size: A. increases only. B. decreases only. C. increases and then decreases. D. decreases and than increases
As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.
This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.
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Please help need by tomorrow it would be very very very appreciated
The linear inequality for the graph in this problem is given as follows:
y ≥ 2x/3 + 1.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:
b = 1.
When x increases by 3, y increases by 2, hence the slope m is given as follows:
m = 2/3.
Then the linear function is given as follows:
y = 2x/3 + 1.
Numbers above the solid line are graphed, hence the inequality is given as follows:
y ≥ 2x/3 + 1.
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Which choices are equivalent to the quotient below? Check all that apply. √16 √8
The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
How to find the equivalent of a quotient?We want to find the equivalent quotient of the given expression; √16 / √8
Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4
Thus, applying that to our expression gives;
√16/√8 = 4/√8
Now, square root of 8 which is √8 can also be expressed as; 2√2
Thus;
4/√8 = 4/2√2 = 2/√2
The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
Step 2: Make sure all radicals are simplified.
Step 3: Simplify the fraction if needed.
If we rationalize the denominator of our expression, we have;
2/√2 × √2/√2 = 2√2/ 2 = √2
Also, 2/√2 can be expressed as √4 /√2
Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
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A steel manufacturer wants to produce a container in the shape of a rectangular solid with volume 84m^3 , the manufacturer wants the length of the container to be one meter longer than the width ,and the height to be one meter greater than twice the width. What should the dimensions of the container be ?
The dimensions of the container should be approximately 3.42 meters (width), 4.42 meters (length), and 7.84 meters (height).
Let's start by assigning variables to the dimensions of the rectangular solid. Let's say the width of the container is w meters.
According to the given information, the length of the container is one meter longer than the width, so the length would be w + 1 meters.
The height of the container is one meter greater than twice the width, so the height would be 2w + 1 meters.
To find the dimensions of the container, we need to consider the volume of the rectangular solid. The volume of a rectangular solid is given by the formula V = length × width × height.
Substituting the values we have:
84 = (w + 1) × w × (2w + 1)
Expanding and simplifying the equation:
\(84 = (2w^2 + 3w + w) \times w\\84 = 2w^3 + 3w^2 + w^2\\84 = 2w^3 + 4w^2\)
Rearranging the equation:
\(2w^3 + 4w^2 - 84 = 0\)
Now we can solve this cubic equation to find the value of w. However, solving a cubic equation analytically can be complex. We can use numerical methods or approximation techniques to find the value of w.
By using numerical methods or a graphing calculator, we find that w is approximately equal to 3.42.
Therefore, the width of the container is approximately 3.42 meters. Using this value, we can calculate the length and height of the container:
Length = width + 1 = 3.42 + 1 = 4.42 meters
Height = 2 × width + 1 = 2 × 3.42 + 1 = 7.84 meters
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Reflect the triangle over the y-axis and find the coordinate of the image of point K.
K’(2, 1)
K’(–2, 1)
K’(–2, –1)
K’(2, –1)
K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.
Therefore, the coordinate of the image of point K is K’(-2, 1).
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Add (5x3+7x−8)+(2x3−5x2−x+3).
how can you tell whether a graph is the graph of a function?
A graph is the graph of a function if no vertical line intersects the graph at more than one point. This is because a function is a set of ordered pairs (x, y), where each x-value is paired with a unique y-value. If a vertical line intersects the graph at more than one point, then there is more than one y-value for a given x-value, which violates the definition of a function.
To determine whether a graph is the graph of a function, you can use the vertical line test. The vertical line test is a simple test that involves drawing a vertical line through the graph. If the vertical line intersects the graph at more than one point, then the graph does not represent a function.
If, on the other hand, the vertical line intersects the graph at only one point at any given x-value, then the graph represents a function.
In other words, a graph is the graph of a function if no vertical line intersects the graph at more than one point. This is because a function is a set of ordered pairs (x, y), where each x-value is paired with a unique y-value. If a vertical line intersects the graph at more than one point, then there is more than one y-value for a given x-value, which violates the definition of a function.
It's important to note that a graph may only represent a function on a certain domain, and may not represent a function on a different domain. Additionally, some functions may be represented by more than one graph. However, using the vertical line test is a useful and reliable way to determine whether a given graph represents a function or not.
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A two-digit number is such that the sum of its digits is 11. When the digits of the number are reversed and the number is subtracted from the original number, the result obtained is 9 Find the original number.
By writing and solving a system of equations we will find that the number is 56
So we can write a two-digit number as:
a*10 + b
Where the two digits are a and b.
Here we must have:
a + b = 11
The reversed number is:
b*10 + a
Then we can write the equation:
b*10 + a - a*10 - b = 9
b*9 - a*9 = 9
Then we have a system of two equations:
a + b = 11
b*9 - a*9 = 9
We can divide both sides of the second equation by 9 to get:
b - a = 1
Now we can isolate b to get:
b = 1 + a
Now we can replace this in the other equation.
a + b = a + (1 + a) = 11
2a + 1 = 11
2a = 11 - 1 = 10
a = 10/2 = 5
Now we have the value of a, and we know that:
b = 1 + a = 1 + 5 = 6
Then the two-digit number is:
a*10 + b = 5*10 + 6 = 56
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convert each polar equation to rectangular form. ( a) theta = pi/6 rectangular form / y = (sqrt(3x))/3 (b) r * cos theta = - 7
Converting the polar equation in rectangular equation we have,
(a) the rectangular equation of polar curve θ = π/6 is, x = √3y
(b) the rectangular equation of polar curve r cos θ = - 7 is, x = -7.
(a) Given that the polar equation is, θ = π/6
We know that,
tan θ = y/x
So, y/x = tan π/6
We know the value is, tan π/6 = 1/√3
y/x = 1/√3
x = √3y
So the rectangular equation is, x = √3y
(b) Given the polar equation,
r cos θ = - 7
x = -7
So, the equation in rectangular coordinate is, x = -7.
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Determine the domain of the following graph:
Answer:
Domain [-11, 8]
Step-by-step explanation:
Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis from -11 to +8
the coded values for a measure of brightness in paper (light reflectivity), prepared by two different processes, are as shown in the accompanying table for samples of size 9 drawn randomly from each of the two processes. do the data present sufficient evidence to indicate a difference in locations of brightness measurements for the two processes? give the attained significance level.
The level can be attained by light reflections.
What are light reflections?The law of reflection states that objects can either be observed through the light they emit or, more frequently, through the light they reflect. The law of reflection, which states that the angle of incidence and reflection must be equal, is observed by reflected light.The transition known as reflection flips a shape in a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its reflected point.n mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflectionlearn more about reflections here:
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An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 grams of an alloy that contains 52% copper with 78 grams of pure copper.
Answer:
mass of copper in the resulting mixture = 104 grams of pure copper
Percent of the resulting mixture that is copper = 81.25%
Step-by-step explanation:
The complete question is
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 grams of an alloy that contains 52% copper with 78 grams of pure copper. How many grams of copper are in the resulting mixture? What percent of the resulting mixture is copper?
The original alloy has a mass of 50 grams,
52% of this 50 grams is copper,
mass of copper = 0.52 x 50 = 26 grams
78 grams of pure copper added will bring the mass of copper to..
mass of copper = 26 + 78 = 104 grams of pure copper
After adding 78 grams of copper to the alloy, the resultant mass of the mixture will be = original mass of alloy + mass of the pure copper added
==> 50 + 78 = 128 grams
Percentage of the resulting mixture that is copper = (total mass of copper in the mixture/total mass of mixture x 100%)
==> 104/128 x 100% = 81.25%