Simplify the expression 7X3g
Answer:
21g
Step-by-step explanation:
you multiply the 7 and the 3 together and get 21
Point A(7, 3) is translated to A prime (16, negative 9). Which rule describes the translation? (x, y) right-arrow (x minus 9, y minus 12) (x, y) right-arrow (x minus 9, y + 12) (x, y) right-arrow (x + 9, y + 12) (x, y) right-arrow (x + 9, y minus 12)
Answer:
[tex](x,y) -----> (x+9,y-12)[/tex]
Step-by-step explanation:
we know that
[tex]A(7, 3) ----> A'(16,-9)[/tex]
The rule of the translation is equal to
[tex](x,y) -----> (x+a,y+b)[/tex]
Find the values of a and b
[tex](7,3) -----> (7+a,3+b)[/tex]
we have that
[tex]7+a=16[/tex] ----> [tex]a=16-7=9[/tex]
[tex]3+b=-9[/tex] ---->[tex]b=-9-3=-12[/tex]
substitute the values of a and b
[tex](x,y) -----> (x+9,y-12)[/tex]
That means----> The translation is 9 units right and 12 units down
Answer:
Option D:
(x, y) -> (x + 9, y minus 12)
Step-by-step explanation: Honestly all people want are the answers so I don't really care to write an explanation.
Which pair of segments in the figures below are congruent?
AB and JK
AB and PN
BC and MN
BC and PN
Answer:
D.BC and Pn are corgruent.
Step-by-step explanation:
Pair of segments in the figures that are congruent : BC and PN.
What is congruence?In geometry, congruent means identical in shape and size. Congruence can be applied to line segments, angles, and figures. Any two line segments are said to be congruent if they are equal in length.
Given in the figure,
Two polygons ABCDEF and JKLMNP
where
AB≅MN
BC≅PN
CD≅PJ
DE≅JK
EF≅KL
FA≅LM
Hence, BC and PN is the pair of segments in the figures that are congruent.
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The price of a movie ticket increased from $25 to $30 What does this mean about the new price?
Choose the correct answer below
O A. The new price is 80% of the old price because 25-30 s 8. or 80%
OB. The new price is 80% of the old price because the price decreases by 20%, which is subtracted from 100%
OC. The new price is 125% of the old price because the price increases by $5, which is multiplied by the original price 5x 25 = 125%
O D. The new price is 20% of the old price because the price increases by 55 and 55 is 20% of $25
OE. The new price is 120% of the old price because the price increases by 20%, which is added to 100%
O F. The new price is 750% of the old price because 25 x 30 = 750
The correct option will the new price is 120% of the old one because the price increases by 20%, which is added to 100%.
What is percent of change?Percent of change is determined by the difference between the two values divided by the orginal one, then multiplied by 100.
i.e. percent of change=(change in value/original value)*100
So according to the asked question,
old value of the shoes=$25
new value of the shoes=$30
change in value=30-25=$5
percent of change=((30-25)/25)*100=20%
hence price increases by 20%.
If the old price is 100 and price increases by 20% then new price will be 120.
So the new price is 120% of the old one.
in another way we can calculate that
old value*x%=new value
⇒old value*x/100=new value
⇒x=new value*100/old value=30*100/25=120%
Therefore the new price is 120% of the old one because the price increases by 20%, which is added to 100%.
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Match each three-dimensional figure to its volume based on the given dimensions. (Assume T = 3.14.)
a right cylinder with radius 4 cm
and height 3 cm
314 cu cm
a cone with radius 5 cm and
height 12 cm
160 cu cm
a pyramid with base area
16 sq cm and height 30 cm
48 cu cm
a pyramid with a square base of
length 3 cm and height 16 cm
150.72 cu cm
A right circular cylinder with radius 4 cm and height 3 cm-150.72 cu cm
A cone with radius 5cm and height 12 cm-314 cu cm
A pyramid with base area 16 sq cm and height 30 cm-160 cu cm
A pyramid with a square base of length 3 cm and height 16 cm-48 cu cm
Explanation
volume of cylinder=[tex]\pi r^2h[/tex][tex]3.14*4^2*3=150.72[/tex] cu cm
volume of cone=[tex]1/3 \pi r^2 h[/tex]=314 cu cm
volume of pyramid=[tex](base area*height)/3=(16*30)/3[/tex]=160 cu cm
volume of pyramid=
=[tex](base area*height)/3\\square base length=3 cm\\base area=a^2 =3^2 =9\\volume=(9*16)/3=48cm^3[/tex]
What is an equation that passes through the points (3,8) and (1,0)
Answer:
y=4x-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(0-8)/(1-3)
m=-8/-2
m=4
y-y1=m(x-x1)
y-8=4(x-3)
y=4x-12+8
y=4x-4
Answer:y - 4x + 4 = 0
Step-by-step explanation: Formula for equation of a line passing through two coordinates is
y - y₁ y₂ - y₁
______ = ______
x - x₁ x₂ - x₁
Therefore, y₂ -y₁
y - y₁ = ____ × ( x - x₁ )
x₂ - x₁
where x₁ =3, y₁ =8, x₂ = 1 and y₂ 0
Now substitute for the value
y - 8 = 0 - 8
______ x ( x - 3 )
1 - 3
Therefore y - 8 = -8/-2 × (x - 3 )
y - 8 = -8/-2 × (x - 3)
y -8 = 4 × (x - 3 )
y - 8 = 4( x - 3 )
y - 8 = 4x - 12, when the brackets are open,
So y = 4x - 12 + 8
y = 4x - 4
Therefore the equation of the line is
y - 4x + 4 = 0
If you have 3 quarters, 5 dimes, and 2 nickels in
your pocket what is the probability you will pick a
dime and then a quarter without putting the dime
back in your pocket?
Answer:
Step-by-step explanation:
No. Of quarters n(Q)= 3
No. Of dimes n(D) = 5
No. Of nickels n(N) = 2
Total T = 3+5+2 = 10
Prob(D) = n(D)/T = 5/10 = 1/2
Now there are 9 left since it is not replaced back
Prob(Q) = 3/9 = 1/3
Prob(D and Q) = 1/2 × 1/3 = 1/6
The probability you will pick a dime and then a quarter without putting the dime back in your pocket is 1/6
What is probability?Probability is the likelihood or chance that an event will occur
If you have 3 quarters, 5 dimes, and 2 nickels in your pocket, the total coins you have will be:
Total outcome = 3 + 5 + 2
Total outcome = 10
Probability of picking a dime = 5/10 = 1/2
Probability of picking a quarter = 3/9 = 1/3
Pr( a dime and then a quarter without putting the dime back in your pocket) = 1/2 * 1/3 = 1/6
Hence the probability you will pick a dime and then a quarter without putting the dime back in your pocket is 1/6
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The weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 220 tons, find the weight of each.
Answer:
A is 198
B is 22
Step-by-step explanation:
22 × 9 = 198
22 + 198 = 220
The country of Sylvania has decided to reduce the number of its illiterate citizens by 3/5 each year. This year there are 9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today. asking for khan
The function to calculate the number of illiterate people in Sylvania t years from today is P(t) = 9000 * (3/5)^t.
Explanation:To write a function that gives the number of illiterate people in Sylvania, P(t), t years from today, we can use the following formula:
P(t) = 9000 * (3/5)^t
This formula represents the reduction in the number of illiterate people by 3/5 each year. To calculate the number of illiterate people t years from today, we multiply the initial number of illiterate people (9000) by the reduction factor (3/5) raised to the power of t.
Answer: 9000( 1 - 3/5 ) ^t
Point J is the midpoint of segment FG with endpoints F(1,4) and G(5,12). Point K is the midpoint of segment GH with endpoints G(5,12) and H(-1,4). What is the measure of JK?
Answer:
1 unit
Step-by-step explanation:
If point J is the midpoint of segment FG with endpoints F(1,4) and G(5,12), then its coordinates are
[tex]x_J=\dfrac{x_F+x_G}{2}=\dfrac{1+5}{2}=3\\ \\y_J=\dfrac{y_F+y_G}{2}=\dfrac{4+12}{2}=8[/tex]
If point K is the midpoint of segment GH with endpoints G(5,12) and H(-1,4), then its coordinates are
[tex]x_K=\dfrac{x_G+x_H}{2}=\dfrac{5+(-1)}{2}=2\\ \\y_K=\dfrac{y_G+y_H}{2}=\dfrac{12+4}{2}=8[/tex]
The measure of JK is
[tex]JK=\sqrt{(3-2)^2+(8-8)^2}=\sqrt{1^2+0^2}=1\ unit[/tex]
Given the coordinates of their endpoints, you find that the points of interest, J and K, have coordinates J(3,8) and K(2,8), respectively. You can then apply the distance formula to find the distance between these two points, resulting in 1.
Explanation:To find the distance between two points, we can apply the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Given that J is the midpoint of FG, the coordinates of J can be found using the midpoint formula ((x1 + x2) / 2, (y1 + y2) / 2). By applying this formula, we find that J = ((1 + 5) / 2, (4 + 12) / 2) = (3,8).
Similarly, the coordinates of K, as the midpoint of GH, are K = ((5 + (-1)) / 2, (12 + 4) / 2) = (2,8).
Now we can plug the coordinates of J and K into the distance formula to find JK: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((2 - 3)^2 + (8 - 8)^2) = sqrt((1)^2 + 0) = sqrt(1) = 1.
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Consider the following piece-wise function. Which of the below correctly describes the graph shown?
Answer:
C
Step-by-step explanation:
The function is formed of 2 straight lines
The equation of a straight line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate the slope using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (2, - 2) ← endpoints of left line
m = [tex]\frac{-2+5}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 for x < 2 ( arrow on line points left )
Repeat
with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (3, 1) ← 2 points on right line
m = [tex]\frac{1+2}{3-2}[/tex] = [tex]\frac{3}{1}[/tex] = 3, thus
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 1), then
1 = 9 + c ⇒ c = 1 - 9 = - 8
y = 3x - 8 for x ≥ 2 ( arrow on line points right )
pls HELP ive been trying to figure this out forever!!!
The solution set for -18 < 5 x - 3 is _____.
a. -3 < x
b. 3 < x
c. -3 > x
d. 3 > x
Answer:
I think is B .3 < x
hope it helps!
Answer:
-3< X is the correct answer. sorry if i'm to late:(
Step-by-step explanation:
Describe the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z”
Answer:
1. Translation 5 units to the left and 1 unit down
2. Reflection across the x-axis
Step-by-step explanation:
Triangle XYZ has its vertices at points X(-6,2), Y(-4,7) and Z(-2,2).
1. Translate triangle XYZ 5 units to the left and 1 unit down. This translation has the rule:
[tex](x,y)\rightarrow (x-5,y-1)[/tex]
Then
[tex]X(-6,2)\rightarrow X'(-11,1);[/tex]
[tex]Y(-4,7)\rightarrow Y'(-9,6);[/tex]
[tex]Z(-2,2)\rightarrow Z'(-7,1).[/tex]
2. Reflect triangle X'Y'Z' across the x-axis. This reflection has the rule:
[tex](x,y)\rightarrow (x,-y)[/tex]
Then
[tex]X'(-11,1)\rightarrow X''(-11,-1);[/tex]
[tex]Y'(-9,6)\rightarrow Y''(-9,-6);[/tex]
[tex]Z'(-7,1)\rightarrow Z''(-7,-1)[/tex]
These points are exactly the vertices of the triangle X''Y''Z''.
The sequence of transformations is translation, rotation, reflection, and dilation.
Explanation:The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is:
Translation: Move the triangle in a linear direction without rotating it.
Rotation: Rotate the triangle about a fixed point or axis.
Reflection: Mirror the triangle across a line known as the axis of reflection.
Dilation: Increase or decrease the size of the triangle while preserving its shape.
By applying these transformations in the specified sequence, triangle XYZ can be mapped onto triangle X"Y"Z".
How do the values of the 4s in 64.723 and 9.048 compare? Select from the drop-down menu to correctly complete the statement. The value of the 4 in 64.723 is times the value of the 4 in 9.048. choose 10 100 1,000
Answer:
Dividing 4 × 1 by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100
Step-by-step explanation:
i) the value of 4 in 64.723 is given by 4 × 1 = 4, because 4 is the one's place
ii) the value of 4 in 9.048 is is given by 4 × 0.01 = [tex]\dfrac{4}{100}[/tex] = 0.04, because 4 is in the hundredth's place
iii) the value of 4 in 64.723 is 100 times the value of 4 in 9.048 which we get by dividing 4 × 1 by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100
Answer:
100
Step-by-step explanation:
AGAIN this is the like the 5th time trying to get an answer and I am so tired and I just want to sleep but I have to finish this so please can someone help me with this 7th grade math homework
Solve by elimination. 4x=14-3y 3x-3y=11
Solving by elimination...
4x=14-3y ---> 12x=42-9y
×3
3x-3y=11 ----> 12x-12y=44
×4
12x=42-9y
-(12x-12y=44)
--------------------
12y=-2-9y
21y=-2
y=-2/21
3x-3(-2/21)=11
3x+2/7=11
3x=10 5/7
x=25/7
Answer:
4x=14-3y 3x-3y=11
Step-by-step explanation:
Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.
What is the greatest possible whole-number length of the unknown side?
The greatest whole possible whole number length of the unknown side is 9 inches
Solution:
Two sides of an acute triangle measure 5 inches and 8 inches
The length of the longest side is unknown
We have to find the length of unknown side
The longest side of any triangle is a hypotenuse
For a acute triangle we know:
If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition that relates these three sides are given as:
[tex]c^2<a^2+b^2[/tex]
Here in this sum,
a = 5 inches
b = 8 inches
c = ?
Substituting we get,
[tex]c^2< 5^2+8^2\\\\c^2 < 25 + 64\\\\c^2 < 89\\\\c < 9.4[/tex]
On rounding to nearest whole number,
c < 9
Hence, to the greatest whole possible whole number length of the unknown side is 9 inches
Answer:
The greatest whole possible whole number length of the unknown side is 9 inches
Step-by-step explanation:
Are 4(3y-2) and 12y-8 equivalent
Answer:
Yes! 4(3y-2)=12y-8
Answer:
yes 4(3y - 2) = (12y - 8)
Step-by-step explanation:
because if you should expand 4(3y - 2) by multiplying each value within the bracket by 4, you will have 12y - 8
52 is 0.4% of what number?
What scale factor is applied to shape B to make shape A
(A) 8 , 6 , 2 , 2
(B) 12, 9 , 3 , 3
To find the scale factor, compare the corresponding dimensions of the two shapes. Divide the dimension of shape A by the corresponding dimension of shape B to calculate the scale factor.
Explanation:In order to find the scale factor applied to shape B to make shape A, we need to compare the corresponding dimensions of the two shapes. The scale factor is determined by dividing the dimension of shape A by the corresponding dimension of shape B. In this case, we compare the lengths of the shapes, so the scale factor is determined by dividing the length of shape A by the length of shape B.
Let's calculate the scale factor:
For the length: A/B = 8/12 = 2/3For the width: A/B = 6/9 = 2/3For the height: A/B = 2/3 = 2/3Therefore, the scale factor is 2/3 for all dimensions of shape B to make shape A.
Two angles in a triangle measure 28 degrees and 93 degrees. What is the measure of the third angle?
59 degrees
87 degrees
121 degrees
152 degrees
Answer:
59
Step-by-step explanation:
The three interior angles in a triangle will always add up to 180°, so:
180-93-28=59
The measure of the third angle is 59 degrees.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given are two angles of a triangle.
First angle = 28 degrees
Second angle = 93 degrees
We know that, the sum of the all the three interior angles of a triangle is 180 degrees.
Let x be the measure of third angle.
x + 28 + 93 = 180
x + 121 = 180
Subtracting 121 from both sides,
x = 180 - 121 = 59 degrees
Hence the third angle is 59 degrees.
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Solve y=4x+8x for x
Answer:
x = y/12
Step-by-step explanation:
Rewrite the equation by completing the square.
4x^2 + 28x + 49=0
Answer:
[tex]4(x+3.5)^{2}=0[/tex]
Step-by-step explanation:
we have
[tex]4x^{2}+28x+49=0[/tex]
step 1
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](4x^{2}+28x)=-49[/tex]
step 2
Factor the leading coefficient
[tex]4(x^{2}+7x)=-49[/tex]
step 3
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]4(x^{2}+7x+3.5^2)=-49+(3.5^2)(4)[/tex]
[tex]4(x^{2}+7x+12.25)=0[/tex]
step 4
Rewrite as perfect squares
[tex]4(x+3.5)^{2}=0[/tex]
The equation by completing the square is [tex]\[ (x + \frac{7}{2})^2 = 0 \].[/tex]
To complete the square for the quadratic equation [tex]\(4x^2 + 28x + 49 = 0\)[/tex], we need to follow these steps:
Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. This gives us:
[tex]\[ x^2 + 7x + \frac{49}{4} = 0 \][/tex]
Next, we need to find the value to complete the square. This is done by taking half of the coefficient of [tex]\(x\)[/tex], which is [tex]\(\frac{7}{2}\)[/tex], and squaring it:
[tex]\[ \left(\frac{7}{2}\right)^2 = \frac{49}{4} \][/tex]
We add and subtract this value to the equation to complete the square:
[tex]\[ x^2 + 7x + \frac{49}{4} - \frac{49}{4} + \frac{49}{4} = 0 \][/tex]
Now, we can rewrite the equation as a perfect square trinomial and a constant:
[tex]\[ (x + \frac{7}{2})^2 - \frac{49}{4} + \frac{49}{4} = 0 \][/tex]
Simplify the equation by combining the constants:
[tex]\[ (x + \frac{7}{2})^2 = 0 \][/tex]
Two students are asked to come to the board to work a math problem. Each student could work an easy question (E) or a hard question (H). Drag and drop the letters to show all the possible outcomes for the students' choices. List the first student's choice followed by the second student's choice.
Answer:
E
Step-by-step explanation:
Javier bought a microwave for $105.The cost was 30% off the original price.what was the price of the microwave before the sale
Answer:
$ 150
Step-by-step explanation:
Given:
Cost price of a microwave = $105
Discount % = 30
Question asked:
what was the price of the microwave before sale = ?
Solution:
Let the price of the microwave before sale = [tex]x[/tex]
Price before sale - 30 % discount = cost price of microwave (by Javier)
[tex]x - 30\% of x = 105[/tex]
[tex]x - \frac{30x}{100} = 105[/tex]
[tex]\frac{70x}{100} = 105\\[/tex]
Multiplying both side by 100
[tex]70x = 105 \times 100[/tex]
[tex]70x = 10500[/tex]
Dividing both side by 70
[tex]x = \frac{10500}{70} \\x = 150[/tex]
x = price of the microwave before sale = $ 150
Thus, price of the microwave before the sale = $150
Identify all points and line segments in the picture below.
Ronnie's dog eats 1/2 of a pound of food each day. Ronnie has a bag containing 4 1/2 pounds of dog food. How many days will the bag feed Ronnie's dog?
4 5 6 7 8 9 10
TIME REMAINING
59:55
A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 9), (2, negative 6), (negative 5, 4), (1, 2), (6, 0).
What is the domain of the function shown in the mapping
Answer:
Step-by-step explanation:
(-3,-9) , (2,-6), (-5,4), (1,2), (6,0)
the domain is gonna be ur x values
so the domain of this function is [ -5,-3,1,2,6] <==
** the domain is ur x values and the range is ur y values
Answer: -1
Step-by-step explanation:
i just answered if off of edg.
Sum of first 1000 consecutive odd counting numbers
Answer:
100,000,000
Step-by-step explanation:
did some research to solve this one, i recommend looking more into to it to ensure that this is the correct answer ;)
The sum of the first 1000 consecutive odd counting numbers is 1,000,000.
To find the sum of the first 1000 consecutive odd counting numbers, we need to recognize a pattern and utilize a simple formula.
Step 1: Identify the Sequence of Odd Numbers
The first few odd counting numbers are:
1, 3, 5, 7, 9, 11, 13, ...
Step 2: Determine the Formula for the Sum
The sum of the first n odd counting numbers can be calculated using the formula:
Sum = n²
This means that the sum of the first n consecutive odd numbers is equal to the square of n.
Step 3: Apply the Formula to Our Problem
In this case, we want to find the sum of the first 1000 odd numbers. Therefore, we set n to 1000:
Sum = 1000²
Step 4: Calculate the Value
Now, we perform the calculation:
Sum = 1000 * 1000 = 1,000,000
If the volume of the crystal ball is about 113 14 cm", the radius of the ball is approximately 3 cm. (Use = 7.)
If the vacant space inside the box were filled with spray foam, the approximate volume of foam required would be___
cm^3.
Answer:
The volume of required foam is 0.1 cm³
Step-by-step explanation:
Given as :
The volume of box = v = 113.14 cm³
The radius of the crystal ball = r = 3 cm
Let The volume of required foam = V cm³
According to question
Volume of crystal ball = [tex]\dfrac{4}{3}[/tex] × π × radius³ where π = 3.14
i.e Volume of ball = [tex]\dfrac{4}{3}[/tex] × π × 3³
Or, Volume of ball = [tex]\dfrac{4}{3}[/tex] × π × 27
Or, Volume of ball = [tex]\dfrac{4}{3}[/tex] × 3.14 × 27
Or, Volume of ball = 4 × 3.14 × 9
Or, Volume of ball = 113.04 cm³
Again
∵ volume of crystal ball = v' = 113.04 cm³
So , The volume of required foam = volume of box - volume of crystal ball
Or, V = v - v'
Or, V = 113.14 cm³ - 113.04 cm³
∴ V = 0.1 cm³
So, The volume of required foam = V = 0.1 cm³
Hence, The volume of required foam is 0.1 cm³ . Answer
Answer:
B and B for plato
Step-by-step explanation: