A ratio shows us the number of times a number contains another number. Caitlin is right.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,
M/S = 2/5
M = 2S/5
After 8 years, their ages will be in the ratio 1:2, therefore,
(M+8)/(S+8) = 1/2
2M + 16 = S + 8
2M - S = -16 + 8
Substitute the value of M,
2(2S/5) - S = -8
-0.2S = -8
S = 40
Now, if we substitute the value of S in the first ratio,
M/S = 2/5
M/40 = 2/5
M = 16
Now, if we take the difference in their ages the difference will be 24(40-16).
Since the difference is 24, we can conclude that Caitlin is right.
Hence, Caitlin is right.
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help me pleaseeeeeeeeeeeeeee
Answer:
C
Step-by-step explanation:
Evaluating the options :
Option A
⇒ 5/2x + 7/2 = 3/4x + 14
⇒ 2.5x - 0.75x = 14 - 3.5
⇒ 1.75x = 10.5
⇒ x = 6
⇒ No ×
===========================================================
Option B
⇒ 5/4x - 9 = 3/2x - 12
⇒ 1.5x - 1.25x = -9 + 12
⇒ 0.25x = 3
⇒ x = 12
⇒ No ×
=========================================================
Option C
⇒ 5/4x - 2 = 3/2x - 4
⇒ 1.5x - 1.25x = -2 + 4
⇒ 0.25x = 2
⇒ x = 8
⇒ Yes √
C is the right answer.
Please solve the question in the picture
Answer:
A. 11"
B. 39"
25 - 15 < x < 25 + 15
10 < x < 40
*x = whole number
Answer:
shortest: 11 incheslongest: 39 inchesStep-by-step explanation:
Given two side lengths for a triangle, the triangle inequality tells you the third side must have a length between the difference and the sum of the given sides.
__
A. minimum lengthThe difference of the given sides 25 and 15 is ...
25 -15 = 10
The smallest integer greater than 10 is 11.
The third side must be at least 11 inches long.
__
B. maximum lengthThe sum of the given sides is ...
25 +15 = 40
The largest integer smaller than 40 is 39.
The third side must be at most 39 inches long.
_____
Additional comment
Formally, the triangle inequality tells you that sides a, b, c must satisfy ...
a +b > c and b +c > a and c +a > b
When we're considering the length of third side (c), there are 3 cases to consider. 1) c is shortest; 2) c is between the other lengths; 3) c is longest. Without loss of generality, we can assume a > b.
1) c is shortest:
a+b>c is always true. b+c>a ⇒ c>a-b (the positive difference)c+a>b ⇒ c>b-a (the negative difference)conclusion: c > a-b
2) a > c > b:
a+b>c is always true. b+c>a ⇒ c>a-b (the positive difference) c+a>b ⇒ c>b-a (the negative difference)conclusion: c > a-b
3) c is longest:
a+b>c (the sum)b+c>a ⇒ c>a-b (the difference will be less than the sum)c+a>b ⇒ c>b-a (the negative difference will be less than the sum)conclusion: a -b < c < a+b . . . . . . for a>b
53° 44°
xº
X=
46°
degrees
A quadrilateral has rotational symmetry of order 2 and no line of symmetry. What is the name of this quadrilateral?
a. square
b. rectangle
c. parallelogram
d. rhombus
Answer:
c
Step-by-step explanation:
paralallegram can be anything with parrell lines
Answer:
C
Step-by-step explanation:
A quadrilateral has rotational symmetry of order 2 and no line of symmetry.
A parallelogram has no lines of symmetry because it is impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other.
In triangle RTS △RTS shown below, point U is on
ST, and point V is on RT so that angle RST UVT∠RST≅∠UVT. If ST=13 VT=5, and RV=13.2, find the length of TU. Figures are not necessarily drawn to scale.
Answer: 7
Step-by-step explanation:
As [tex]\angle T \cong \angle T[/tex] by the reflexive property, we know that [tex]\triangle RST \sim \triangle UVT[/tex] by AA.
Since corresponding sides of similar triangles are proportional,
[tex]\frac{UT}{5}=\frac{13.2+5}{13}\\UT=(5)\left(\frac{13.2+5}{13} \right)=\boxed{7}[/tex]
Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.
Answer:
Hi,
a=b+3
Step-by-step explanation:
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]
Thus:
c+2b+8-4a=c-a-b-1
3b-3a=-9
a=b+3
How does the volume of the larger cube compare to the volume of the smaller cube? Use pencil and
paper. Use this and other examples to describe what happens to the volume of a cube if you triple the length
of the edges.
Answer:
Option C, The volume of the length cube is 3 times the volume of the smaller cube
Step-by-step explanation:
21.8 / 7.8 = 2.8
the volume of the larger would be 21.8^3 = 10360.23
the volume of the larger would be 7.8^3 = 474.55
Find the mean and median of the data. 31, 14, 18, 26, 17, 32
Answer:
The mean is 23
The median is 22
Step-by-step explanation:
To find the mean you have to do 2 steps:
Step 1: Add up all your numbers:
31 + 14 + 26 + 17 + 32 + 18
= 138
Step 2: Divide you answer by how many numbers there are(6):
138 ÷ 6
= 23
Now to find you median
First put the numbers in order:
14, 17, 18, 26, 31, 32
Now grab the middle number and since there are an even amount of numbers grab the 2 middle numbers:
14, 17, 18, 26, 31, 32
Now add the 2 numbers:
18 + 26
= 44
The last step is to divide your answer by 2:
44 ÷ 2
= 22
A bottle contains 20 blue bags and 15 red bags. If two bags are picked at random one after the other with replacement, what is the probability that the first bag is blue and then red?
Answer:
12÷49Step-by-step explanation:
The total number of bags in the bottle = 20 + 15 = 35
Then
the probability that the first bag is blue = 20/35
If we replace the first bag :
the probability that the second (picked) bag is blue = 15/35
Conclusion:
If two bags are picked at random one after the other with replacement
Then
the probability that the first bag is blue and then red is :
(20÷35)×(15÷35)
= (4÷7)×(3÷7)
= 12÷49
= 0.244897959184
Find the x-intercept and y-intercept of the equation: 3x-y = -9
The x-intercept and y-intercept of the equation: 3x - y = -9 is -3 and 9 respectively.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have equation:
3x - y = -9
The above equation represents a linear equation;
The equation can be written as:
y = 3x + 9
To find the x-intercept plug y = 0
x = -3
To find the y-intercept plug x = 0
y = 9
Thus, the x-intercept and y-intercept of the equation: 3x - y = -9 is -3 and 9 respectively.
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What is the equivalent to a dash?
Answer:
a dash is 1/8 tsp.
Step-by-step explanation:
a dash is 1/8 tsp or called 0.13
A. The graph is translated 2units down.
B. The graph is translated 2 units left.
C. The graph is translated 2 units right.
D. The graph is translated 2 units up.
Answer:
c
Step-by-step explanation:
the -2 causes a shift 2 units right
can someone help with this please
Answer:
Step-by-step explanation:
whitch of the following is closest to 8 62 61 65 66
Answer:
If the question is which is closest to 8, the answer is 61
Step-by-step explanation:
Susan collects softball cards in her collection she had 128 she decides to gives 3 eights
Answer:
need more information to answer for you.
Step-by-step explanation:
What is Parabola?
What is the transformation of parabolas?
Answer:
What is Parabola:
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
What is the transformation of parabolas?
The function y=x2+b has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards. Similarly, we can translate the parabola horizontally
Step-by-step explanation:
question 3 help me please
Answer:
3x+(4x-1)+90°=180°{sum of angles in a triangle}
3x+4x-1+90°=180°
7x+89°=180°
7x=180°-89°
7x=91°
divide both sides by 7
x=13
Answer:
The answer is x=13
PLEASE HELP ASAP MARKING BRAINLEIST + 50 POINTS
Answer:
scale factor = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{V'W'}{VW}[/tex] = [tex]\frac{1}{5}[/tex]
Katy invests a total of $13,000 in two accounts paying 2% and 7% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $310.00.
Invested at 2%___?
Invested at 7%___?
Answer:
2 % amount = 12000 7% amount = 1000 dollars
Step-by-step explanation:
x = 2% amount
then 13 000 - x = 7% amount
.02x + .07 (13000-x) = 310
-.05x + 910 = 310
.05x = 600
x = 600/.05 = 12000 then the 7% amount is 1000
if the area of a square is 32ft how long is the diagonal?
Answer: 8
Step-by-step explanation:
To find the diagonal, we need to use two formulas:
Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)
Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
Since every side of a square is the same:
[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]
Our equation:
[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]
The picture below visually explains the problem
Hope this helps!
2r + 3s = 14
2( )+ 3s = 14
+3s = 14
3s=
S =
Answer:
4
Step-by-step explanation:
3s=14-2
3s=12
3s/3=12/3
s=4
In the following diagram, BC is parallel to DE.
What is the measure of Zx?
Angles are not necessarily drawn to scale.
W
103°
B
D
4x =
F
42°
H
E
Answer: 35
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].
Sp, by the corresponding angles theorem, x=35
Please answer asap!!!!!! I Inserted photo. Thankssss
Answer:
2nd option
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
given
6xy³z × 3x²yx²
= 6 × 3 × x × x² × x² × y³ × y × z
= 18 × [tex]x^{(1+2+2)}[/tex] × [tex]y^{(3+1)}[/tex] × z
= 18[tex]x^{5}[/tex][tex]y^{4}[/tex]z
Using complete sentences, describe how the variable h and the variable k of the general formula for a cube root function effects the graph. The general formula is y=a^3√ x-h+k
Using translation concepts, it is found that the variables h and k affect the graph of the function as follows:
The function is shifted h units to the right.The function is shift k units up.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we consider the parent cube root function as follows:
[tex]y = \sqrt[3]{x}[/tex]
Then, these following changes happened:
x -> x - h, which means that the function was shifted h units to the right.y -> y + k, which means that the function was shifted k units up.More can be learned about translation concepts at https://brainly.com/question/4521517
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Please help me with this
Answer:
42
Step-by-step explanation:
6 times 7 is 42
the gas tank in minas car holds 15 gallons. Her car gets between 25 and 30 miles to the gallon. If Mina fills up the gas tank and then drives until she runs out of gas, what is the least number of miles she can drive?
A. 300mi
B. 375mi
C. 405mi
D. 450mi
the lowest mileage rate is 25 miles per gallon.
Multiply 25 by 15 gallons
25 x 15 = 375 miles
Answer: B. 375 miles
Divide 8,382 ÷ 7 please answer
Answer:
The answer is 1197.42
Step-by-step explanation:
PLEASE HELP URGENTLY! RIGHT ANSWERS ONLY!
Answer:
Hi! The answer is B!
I would suggest using a graphing calculator to compare all the lines. You can use this free one called Desmos, sorry i was not able to attach a link :)
2/3 - 5/4 + 7/3 whats the4 answer pls
Answer:
7/4Step-by-step explanation:
2/3 - 5/4 + 7/3
=8/12 - 15/12 + 28/12 (LCM=12)
(8 - 15 + 28)/12
=21/12
=7/4
Which graph does not represent a function of x?