Answer:
x = 4, y = 3 → (4, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+3y=17&\text{multiply both sides by (-2)}\\3x+6y=30\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x-6y=-34\\3x+6y=30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\qquad\text{change the signs}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\2(4)+3y=17\\8+3y=17\qquad\text{subtract 8 from both sides}\\3y=9\qquad\text{divide both sides by 3}\\y=3[/tex]
Jonathan's piggy bank contains 20 nickels, 30 quarters, and 50 one-dollar coins. He picks 20 coins from the bank at random; 12 of these coins are one-dollar coins. The theoretical probability of picking a one-dollar coin from the piggy bank before the draw is %, but the experimental probability, based on the draw, is %.
Answer:
Theoretical probability: 50/100 or 50%
Experimental probability: 12/20 or 60%
Step-by-step explanation:
Let's find out both probabilities asked.
Theoretical probability:
In the whole bank, here are 100 coins (20 nickels + 30 quarters + 50 one-dollars), among which there are 50 one-dollar coins. So the probability to pick up a one-dollar coin is 50 out 100, so...
TP = 50/100 or 50%
Experimental probability:
For the experimental probability, we know Jonathan picked out 20 coins, out of which 12 were one-dollar coins, so the probability is 12 out of 20...
EP = 12 / 20 = 60%
Convert the following measurements into the units given in the brackets
a. 8m (mm)
b. 0.02m (mm)
c. 110 000 mm (m)
d. 28 400 cm (km)
e. 0.00001km (cm)
f.62 743 000 mm (km)
g. 5cm (mm)
h. 2.8m (cm)
i . 521cm (mm)
j. 83.7cm (m)
k. 4.6 km (m)
l. 2170m (km)
What of the following best describe XW
XW represents the altitude.
The correct answer is an option (C)
What is median?"It is a line segment that joins a vertex of triangle to the mid-point of the side that is opposite to that vertex."
What is altitude of triangle?"It is the perpendicular drawn from the vertex of the triangle to the opposite side."
What is perpendicular bisector?"A line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. "
What is angle bisector?"A line drawn from the vertex of a triangle to its opposite side such that it divides the angle into two equal or congruent angles."
for given question,
XW is altitude of triangle XYZ.
Therefore the correct answer is an option (C)
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( NEED ANSWER NOW ) How many possible outcomes exist when Louisa spins the spinner below twice?
A. 8
B. 10
C. 16
D. 64
Answer:
Step-by-step explanation:
64
There are 8 numbers on the spinner.
The first spinner could be 1 of 8 and the second spin could also be 1 of 8.
To find the total outcomes, multiply the number of outcomes of each spin by each other.
Spin 1 : 8 out comes
Spin 2: 8 outcomes
Total outcomes = 8 x 8 = 64
The answer is D. 64
circle o has a circumfrence of approximately 44 in. what is the approximate lenght of the diameter d?
-7in
-14in
-22in
-44in
Answer:
14 inch
Step-by-step explanation:
formula for circumference:
2(pi)r @ (pi)d
*where: r = radius
d= diameter
pi used = 22/7
22/7 x d = 44
d= 44/ (22/7)
=14
2/1 = 8x - 2/ 9 ! help
Answer: 5/2
Step-by-step explanation:
Cross multiply
18 = 8x - 2
20 = 8x
20/8 reduces to 5/2
Answer:
x = 5/2
Step-by-step explanation:
Step 1: Cross multiply
18 = 8x - 2
Step 2: Use the Addition Property of Equality
20 = 8x
Step 3: Use the Division Division Property of Equality
20/8 = x
Step 4: Simplify
5/2 = x
Which of the following equations represents a line that is perpendicular to
y = -4x+9 and passes through the point, (4, 5)?
A. y- x+5 B. y- *x+6
C. y = x+4 D. y --4x+4
For this case we have that if two lines are perpendicular, then the product of their slopes is -1.
If we have the following equation of the line:
[tex]y = -4x + 9[/tex]
The slope is [tex]m_ {1} = - 4[/tex]
Then yes:
[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 4}\\m_ {2} = \frac {1} {4}[/tex]
The equation of the new line will be:
[tex]y = \frac {1} {4} x + b[/tex]
We substitute the point to find "b":
[tex]5 = \frac {1} {4} (4) + b\\5 = 1 + b\\b = 5-1\\b = 4[/tex]
Finally, the equation is:
[tex]y = \frac {1} {4} x + 4[/tex]
Answer:
[tex]y = \frac {1} {4} x + 4[/tex]
If the slope of GH is −4/5 and the slope of HJ is 3/4, find the slope of JK so that GHJK is a parallelogram. quick answer pls
Answer:
Slope of JK = -4/5
Step-by-step explanation:
We know that GHJK is a parallelogram. If GHJK is a parallelogram then the sides of parallelogram will be:
GH, HJ, JK, GK
Hence the opposite sides will be:
GH and JK
HJ and GK
We know that opposite sides of parallelogram are parallel to each other and the slopes of parallel lines is equal.
So the slope of GH and JK will be equal.
And slopes of HJ and GK will be equal.
As we are given the slope of GH which is -4/5, the slope of JK will also be -4/5 because both lines are parallel.
21. How many times larger is the volume of a cone if the height is multiplied by 3?
The volume of a cone increases by a factor of 27 when its height is multiplied by 3, as the volume of a cone scales with the cube of its linear dimensions.
The question asks how many times larger the volume of a cone becomes if its height is multiplied by 3. The volume of a cone is given by the formula V = ([tex]\frac{1}{3}[/tex]1/3)πr²h, where r is the radius and h is the height. If you multiply the height by 3, the volume will increase by a factor of 3 since volume scales with the third power of the linear dimensions. Therefore, the new volume would be 3³, or 27 times the original volume. This result can also be demonstrated by the mathematical expression Vnew = ([tex]\frac{1}{3}[/tex])πr²(3h) = 27Voriginal.
If 2x + y = 6 and m - n = 2, what is the value of (4x + 2y)(4m - 4n)
Answer:
96
Step-by-step explanation:
If m - n = 2, then 4m - 4n = 4(m - n) = 4(2).
Then (4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y).
But we are told that 2x + y = 6. Multiplying all terms by 2, we get
4x + 2y = 12. Substituting 12 for 4x + 2y, we get our final answer:
(4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y), or 8(12) = 96
Answer:
96
Step-by-step explanation:
(4x + 2y)(4m - 4n) = ?
We have an equation
2x+y =6
Multiply it by 2
2(2x+y) = 2*6
Distribute
4x+2y = 12
Substitute 12 in for 4x+2y into the original problem
12(4m - 4n) = ?
We have an equation
m-n = 2
Multiply this by 4
4(m-n) = 4*2
Distribute
4m-4n = 8
Substitute 8 in for 4m -4n in 12(4m - 4n) = ?
12 * 8 = ?
96
X+y-3z=8
Slove for x
[tex]x+y-3z=8\\x=-y+3z+8[/tex]
What is the range of the following data set?
7.7, 8.4, 9, 8, 6.9
0.8
2.1
0.4
1.4
I am pretty sure its 2.1
The range is given by: largest number in the data set - smallest number in the data set.
In our case, the largest value is 9 and the smallest value is 6.9. Therefor:
Range = 9 - 6.9 = 2.1
Thus, you have correctly identified the answer as the second choice (2.1). It is easy to get confused with much larger data sets but always keep in mind that the range is simply the largest value minus the smallest value. This makes sense since 'range' refers to the spread in something, for example if you were testing your vocal range you would find the highest note you could sing and the lowest note - this is the same here, we are just finding the range of a data set instead.
Answer:
The correct answer is second option
2.1
Step-by-step explanation:
Points to remember
Range of a data set
The range of a data set means that, the difference between the highest and lowest value of the data set.
To find the range of data set
It is given that, a data set
7.7, 8.4, 9, 8, 6.9
Highest value = 9 and lowest value = 6.9
Range = Highest value - lowest value
= 9 - 6.9 = 2.1
Therefore the correct answer is second option
An electrical tower casts a 120-foot shadow. At the same time, a 10-foot
street sign casts a shadow of 8 feet. What is the height of the tower?
Answer:
The height of the tower is 150 ft
Step-by-step explanation:
Let the height of the tower be H feet.
The corresponding sides will then be in the same proportion.
The ratio of the shadows will be in the same proportion as the ratio of the heights.
[tex]\frac{H}{10}=\frac{120}{8}[/tex]
We multiply both sides by 10 to get:
[tex]\frac{H}{10}\times 10=\frac{120}{8}\times 10[/tex]
[tex]H=150[/tex]
Therefore, the height of the tower is 150 ft
Answer:
Height of the tower = 150 foot
Step-by-step explanation:
We need to find height of the tower with 120-foot shadow.
We have a 10-foot street sign casts a shadow of 8 feet.
[tex]\texttt{Ratio of height to shadow height =}\frac{10}{8}=\frac{5}{4}[/tex]
We have
[tex]\frac{\texttt{Height of tower}}{\texttt{Shadow height of tower}}=\frac{5}{4}\\\\\frac{\texttt{Height of tower}}{120}=\frac{5}{4}\\\\\texttt{Height of tower}=\frac{5}{4}\times 120=150feet[/tex]
Height of the tower = 150 foot
True or false? In a mapping diagram, a relation that is a function can have two arrows coming from the same input value.
Answer:
false
Step-by-step explanation:
In a mapping diagram, a relation that is a function can have two arrows coming from the same input value
false
Answer: False.
Step-by-step explanation:
By definition, a relation is a function if each input value has only one output value.
Knowing this, we can say that in a mapping diagram, a function will never have two arrows coming from the same input value.
In other words, if in a mapping diagram a relation has two arrows coming from the same input value, this means that this input value has two output values, and according to the definition mentioned above, this relation cannot be a function.
Therefore, the statement "In a mapping diagram, a relation that is a function can have two arrows coming from the same input value", is FALSE.
A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Create and graph the solution set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x.
The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the initial value of y.
Let y represent the amount of water remaining after x minutes.
Jim's yard contains 60 gallons of water. Hence b = 60.
The water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Hence m = -1/10. The equation is:
y = -(1/10)x + 60
The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60
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The endpoints of a regular pentagon are (-1,4) and (2,3). What is the perimeter of the Pentagon?
1. Square root of 10
2. 5 square root of 10
3. 5 square root of 2
4. 25 square root of 2
the assumption being that the endpoints are two continuous points in the pentagon, Check picture below.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-1)]^2+[3-4]^2}\implies d=\sqrt{(2+1)^2+(3-4)^2} \\\\\\ d=\sqrt{9+1}\implies d=\sqrt{10}~\hfill \stackrel{\stackrel{~\hfill \stackrel{\textit{5 sides}}{}}{\textit{perimeter of the pentagon}}}{5\sqrt{10}}[/tex]
1/2x=1/4 what does x =???
Answer:
x=2
Step-by-step explanation:
First of all cross-multiply.
1/2x=1/4
(1) x (4) =1 x 2x
4=2x
After flip the equation.
2x=4
Then divide both sides by 2.
2x/2=4/2
x=2
The graph of y = ax 2 + bx + c is a parabola that opens up and has a vertex at (-2, 5). What is the solution set of the related equation 0 = ax 2 + bx + c?
Answer:
The solution set is ∅
Step-by-step explanation:
The expression
y = ax^2 + bx + c
is a quadratic equation.
The vertex is located at (-2, 5) and the graph opens up, this means that it never intercepts the x-axis.
The solution set is ∅
Please see attached image
Answer:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Step-by-step explanation:
Assume c = 0
Using the formula for the x-coordinate of the vertex, b can be calculated in terms of a:
[tex]x=\frac{-b}{2a} \\-2=\frac{-b}{2a} \\b=4a[/tex]
B can then be substituted into the quadratic equation, along with the coordinates of the vertex, to solve a:
[tex]y=ax^{2}+bx\\y=ax^{2}+4ax\\5=a(-2)^{2}+4(-2)a\\5=4a-8a\\5=-4a\\a=\frac{5}{-4}[/tex]
AND
[tex]b=4a\\b=\frac{-5}{4} *4\\b=-5[/tex]
Substituting into the quadratic equation:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Because a is negative, the parabola opens up.
what is 16% of 90 helpppp plssss
Answer:
first off, welcome to brainly, second, your answer is 14.4
Step-by-step explanation:
Please someone help me
Answer: Third option.
Step-by-step explanation:
When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.
To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.
Then, the reciprocal of the fraction [tex]\frac{1}{3}[/tex] is:
[tex]\frac{3}{1}=3[/tex]
Therefore, you can find the quotient of [tex]8[/tex]÷[tex]\frac{1}{3}[/tex] by multiplying [tex]8[/tex] by [tex]3[/tex]:
[tex]8[/tex]÷[tex]\frac{1}{3}=8*3=24[/tex]
When dividing fractions these are the steps you will take:
1. The first number in the expression stays the same (if it is a whole number then you may just place a one in the denominator and keep the numerator as the whole number like so)
[tex]\frac{8}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]
2. Change the division sign into a multiplication sign
[tex]\frac{8}{1}[/tex] × [tex]\frac{1}{3}[/tex]
3. Take the reciprocal (switch the places of numerator and denominator) of the second number in the expression
[tex]\frac{8}{1}[/tex] × [tex]\frac{3}{1}[/tex]
4. Multiply across
[tex]\frac{8*3}{1*1}[/tex]
As you can see to find the quotient of [tex]\frac{8}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex] you must multiply 8 by 3 (C)
Hope this helped!
~Just a girl in love with Shawn Mendes
Evaluate this equation: -4(9+5)
Answer:
-56
Step-by-step explanation:
Simplify the following:
-4 (9 + 5)
9 + 5 = 14:
-414
-4×14 = -56:
Answer: -56
a cone has a diameter of 12 and a height of 7 what is the area
[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} \stackrel{\textit{half of diameter}}{r=6~\hfill }\\ h=7 \end{cases}\implies SA=\pi (6)\sqrt{6^2+7^2}+\pi 6^2 \\\\\\ SA=6\pi \sqrt{85}+36\pi \implies SA=6\pi (\sqrt{85}+6)\implies SA\approx 286.88[/tex]
What number must you add to complete the square?
x2 - 18x= 29
Answer:
81
Step-by-step explanation:
Given
x² - 18x = 29
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 9)x + (- 9)² = 29 + (- 9)²
x² + 2(- 9)x + 81 = 29 + 81
(x - 9)² = 110
Answer:
81
Step-by-step explanation:
Simplify the following expression.
Answer:
B.
Step-by-step explanation:
It is just common sense. The top numbers have to be smaller than the top numbers
coven 12 - 31:1-13; wees laula
Iven
WILL GIVE BRAINLIEST PLEASE HELP
I need help please :’( Simplify -4x - x
Answer:
-5x
Step-by-step explanation:
Answer:
-5x
Step-by-step explanation:
-4x-x --------------> factor out the x
= (-4-1) x
= -5x
which choices are equivalent to the exponential expression below? check all that apply. (2/3)^3
A. 6/9
B. (2/3) x (2/3) x (2/3)
C. 8/27
D. 2^3 /3^3
E.16/81
F. 3 x (2/3)
Answer:
B. (2/3) x (2/3) x (2/3)
C. 8/27
D. 2^3 /3^3
Step-by-step explanation:
You need to know the following property
[tex]\LARGE \left(\frac{a}{b} \right)^c = \frac{a^c}{b^c}[/tex]
Exponent also means you're multiplying the same number for an 'n' number of times.
For example, 2^3 = 2 * 2 * 2
we multiply it by itself 3 times since 3 is the exponent.
x^y
x is the base, y is the exponent
we read it as x to the power of y
If the exponent is 2, we say it as x squared
If the exponent is 3, we say it as x cubed
The exponential expression (2/3)^3 is equivalent to options B: (2/3) x (2/3) x (2/3), C: 8/27, and D: 2^3 /3^3, because they all result in the same value.
Explanation:The exponential expression (2/3)^3 can be interpreted as multiplying 2/3 by itself three times. Here's how it works:
(2/3) x (2/3) x (2/3) = 8/27. In other words, 2 cubed (2^3 = 8) divided by 3 cubed (3^3 = 27), which equals 8/27.
So, the equivalent expressions among the given options are:
B. (2/3) x (2/3) x (2/3) C. 8/27 D. 2^3 /3^3 Learn more about Exponential Expressions here:
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Solve the equation x4 – 26x2 + 25 = 0 in the real number system.
Answer:
x = -1, 1, -5 , 5.
Step-by-step explanation:
x4 – 26x2 + 25 = 0
Factoring:
(x^2 - 25)(x^2 - 1) = 0
So x^2 - 25 = 0 gives x^2 = 25 and x = +/- 5.
x^2 - 1 gives x^2 = 1 and x = +/- 1.
Follow below steps:
To solve the equation x4 − 26x2 + 25 = 0, we can use substitution to simplify the equation. Let's set u = x2, which turns our equation into a quadratic form: u2 − 26u + 25 = 0.
Now, we apply the quadratic formula where a = 1, b = -26, and c = 25 to find the values of u. The quadratic formula is u = (-b ± √(b2 - 4ac))/(2a). Substituting the values, we get the roots for u which are u = 25 and u = 1.
Now we substitute back for x by setting x2 = u, which gives us two separate equations to solve: x2 = 25 and x2 = 1. Solving these, we find the solutions for x to be x = 5, x = -5, x = 1, and x = -1.
Marking Brainliest!
Look at polygon ABCD and its translation
If B is 120°, what is the measure of B?
Identify the pairs of rates as equivalent or not equivalent.
Tiles
18/3 and 9/1
32/4 and 8/1
36/6 and 6/1
20/5 and 3/1
35/7 and 5/1
100/10 and 5/1
Boxes
Equivalent pairs
Not Equivalent pairs
ANSWER
See explanation
EXPLANATION
If we can simplify the first fraction to obtain the second fraction, then the two fractions are equivalent pairs
EQUIVALENT PAIRS
[tex] \frac{32}{4} \: and \: \frac{8}{1} [/tex]
[tex]\frac{36}{6} \: and \: \frac{6}{1} [/tex]
[tex]\frac{35}{7} \: and \: \frac{5}{1} [/tex]
NOT EQUIVALENT PAIRS
[tex]\frac{18}{3} \: and \: \frac{9}{1} [/tex]
[tex]\frac{20}{5} \: and \: \frac{3}{1} [/tex]
[tex]\frac{100}{10} \: and \: \frac{5}{1} [/tex]
Answer:
Equivalent pairs
32/4 and 8/1
36/6 and 6/1
35/7 and 5/1
Not Equivalent pairs
18/3 and 9/1
20/5 and 3/1
100/10 and 5/1
Step-by-step explanation:
Equivalent pairs: Those pairs that are different fractions but represent the same number.
1. 18/3 and 9/1
18/3 can be simplified into 6/1
so, 18/3 and 9/1 are not equivalent pairs
2. 32/4 and 8/1
32/4 can be simplified into 8/1
so, 32/4 and 8/1 are equivalent pairs
3. 36/6 and 6/1
36/6 can be simplified into 6/1
so, 36/6 and 6/1 are equivalent pairs
4. 20/5 and 3/1
20/5 can be simplified into 4/1
so, 20/5 and 3/1 are not equivalent pairs
5. 35/7 and 5/1
35/7 can be simplified into 5/1
so, 35/7 and 5/1 are equivalent pairs
6. 100/10 and 5/1
100/10 can be simplified into 10/1
so, 100/10 and 5/1 are not equivalent pairs