Answer: 2:5
Step-by-step explanation:
To find the ratio, we need to find the greatest common factor and divide both of the dimensions by the greatest common factor. In this case 12 is the greatest common factor.
24/12=2
60/12=5
Therefore, the ration that expresses the scale used to create this dimension is 2:5.
Solve this system of equations for x using the addition method.
5x+3y=10
3x-4y=61
Answer:
223/29
Step-by-step explanation:
5x+3y=10 . multiply by 4
3x-4y=61 . multiply by 3
20x+12y=40
+ 9x-12y=183
_____________
29x-0y = 223 . divide both sides by 29
x = 223/29
The midpoint of a segment can be found using the formulas for a directed line segment, x = (x2 – x1) + x1 and y = (y2 – y1) + y1. When using these formulas to find a midpoint, which is true?
The midpoint of a segment can be found using the formula as follows:
mid point = (x₁ + x₂ / 2 , y₁ + y₂ / 2)
How to find the mid point of a segment?The midpoint is the middle point of a line segment.
In other words, the midpoint of a segment is the point on that line segment that divides the segment into two congruent segments.
The mid point of a segment can be represented mathematically as follows:
Hence,
mid point = (x₁ + x₂ / 2 , y₁ + y₂ / 2)
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Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is
Answer:
f(x) = -3x^2 + 10x + 3
Step-by-step explanation:
(0,3) (2,11)(3,6)
Using the form ax^2 + bx + c = y
From the first set we know that c = 3
Write an equation for the last two sets
x=2; y=11
a(2^2) + b(2) + 3 = 11
4a + 2b = 11 - 3
4a + 2b = 8
simplify divide by 2
2a + b = 4
and
x=3, y=6
9a + 3b + 3 = 6
9a + 3b = 6 - 3
9a + 3b = 3
simplify divide by 3
3a + b = 1
:
Use elimination to find a
3a + b = 1
2a + b = 4
--------------subtracting eliminate b
a = -3
Find b using the equation 2a + b = 4
2(-3) + b = 4
b = 4 + 6
b = 10
:
The equation: f(x) = -3x^2 + 10x + 3
ninety-eight thousand ,five (how to write in numerical)?
Answer:
98005
Step-by-step explanation:
ninety-eight thousand = 98000
five = 5
together = 98005
11. Find the solutions of x^2-x-30 = 0.
Please give a walkthrough/step by step I am trying to learn how to do it!
To find the solutions of quadratic equation, there are two ways to do which are:
FactorizeQuadratic FormulaStep 1
- Factor the expression.
To factor the expression, refer below:
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - bx - ax + ab}[/tex]
For bx and ax, both can be common-factored. Therefore
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - (b + a)x + ab}[/tex]
From the above, we conclude that:
The middle term is b+aThe last term is a×bThus, we have to find two numbers that satisfy a+b and a×bFrom the expression, 30 comes from 5×6 and when 5-6 = -1. Therefore, a can be 5 and b can be 6.
[tex] \displaystyle \large{{x}^{2} - x - 30 = (x + 5)(x - 6)}[/tex]
Because in the middle term, it is -x which is negative, we have to let the highest number become negative.
From the factored expression:
The middle term = 5x + (-6x) = -xThe last term = 5 × (-6) = -30Then we replace the standard equation with factored form.
[tex] \displaystyle \large{ (x + 5)(x - 6) = 0}[/tex]
For this part, we solve like a linear equation where we isolate x. Just think you are solving two linear equations!
Hence
[tex] \displaystyle \large{ x = - 5, 6}[/tex]
Therefore, the solutions are x = -5, 6.
15) A small rectangular block of land has a perimeter of 100 m and an area of 225 m². Find the dimensions of the block of land.
Answer:
45 and 5 are the dimensions of the block of land.
Step-by-step explanation:
2(x + y) = 100, x + y = 100/2, y = (50 - x)
xy = 225
x (50 — x) = 225
0 = x^2 — 50x + 225
0 = (x — 45) (x -5)
45 and 5 are the roots of the above polynomial, thus they are the sides or dimensions of the block of land.
In ΔRST, m < R = 104°, r = 20, and t = 10. Find the m < S, to nearest degree.
9514 1404 393
Answer:
47°
Step-by-step explanation:
The law of sines helps you find angle T. From there, you can find angle S.
sin(T)/t = sin(R)/r
sin(T) = (t/r)sin(R) = (10/20)sin(104°)
T = arcsin(sin(104°)/2) ≈ 29°
Then angle S is ...
S = 180° -R -T = 180° -104° -29°
∠S = 47°
I need help with this I don't ever understand rounding.
Round each decimal number to the nearest tenth. Then, select the best estimate for the subtraction equation 1.79 − 0.67 = ___.
1
1.1
1.2
1.3
Answer: 1.12
Step-by-step explanation:
Here 1.79 -0.67 = 1.12 ( if we subtract from the large positive number to a minimum number then it's answer always should be positive value )
Now we are looking for the rounding figure with is very near of it which is 2 decimal or percentage value
For example :
1.444- 0.67 = 0.774 ( Here last digit is 4 so its round will be 0.77)
1.444-0.677 = 0.767 ( Here last digit is 7 so its round will be 0.77)
So we will round the value if it's last digit is greater than or equal to 5 value.
Which statement is true about the climbers’ heights?
What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
15
18
21
27
–
5z2–7z2
Simplified
Answer:
-12z^2
Brainliest, please!
Step-by-step explanation:
-5z^2 - 7z^2 = -12z^2
Can someone help me please :00
Answer:
according to the dark spots which shows where each number goes to, it would be D.-2
Find the LCM of 315,420,525 using prime factorisation method with slove it
[tex]\boxed{\sf \:\begin{cases}\\\begin{gathered} {\underline{{ \sf {\blue{\Large\bf \underbrace{ {\rm {\purple{\begin{array}{r | l}\large\rm{\red{ 5}}&\underline{315,420,525}\\\large\rm{\red{ 3}}& \underline{63,84,105}\\\large\rm{\red{3}}&\underline{21,28,35}\\\large\rm{\red{ 7}}&\underline{7,28,35}\\\large\rm{\red{2}}&\underline{1,4,5}\\\large\rm{\red{2}}&\underline{1,2,5}\\\large\rm{\red{5}}&\underline{1,1,5}\\&1,1,1\end{array}}}}} }}}}}\end{gathered}\\\end{cases}}[/tex]
LCM = 5 × 3 × 3 × 7 × 2 × 2 × 5
LCM = 6300
Hence, the LCM of 315 , 420 , 525 is 6300
Answer:
6300Step-by-step explanation:
Prime factors of given numbers:
315 = 3*3*5*7420 = 2*2*3*5*7525 = 3*5*5*7The LCM is:
LCM(315, 420, 525) = 2*2*3*3*5*5*7 = 6300Consider the points below. P(â1, 4, 1), Q(0, 6, 2), R(4, 3, â1)
a. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
b. Find the area of the triangle PQR.
Answer:
B. Find the area of the triangle PQR.
(2x³)⁴= ? What is the right answer, with full explanation please:
A. 16x⁷
B. 16x¹²
C. 8x⁷
D. 8x¹²
The required simplified value of the given expression is 16x¹². Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
=(2x³)⁴
As we know that,
[xᵃ]ᵇ = xᵃˣᵇ
So,
(2x³)⁴ = 2⁴x³ˣ⁴
= 16x¹²
Thus, the required simplified value of the given expression is 16x¹².
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y + (2/25) = 11/15
What’s y
Answer:
[tex]\frac{49}{75}[/tex]
Step-by-step explanation:
y= [tex]\frac{11}{15}[/tex]-[tex]\frac{2}{25}[/tex]
y= [tex]\frac{49}{75}[/tex]
Answer:
49/75
Step-by-step explanation:
y + 2/25 = 11/15
now, we could do it like the other answer and do fraction arithmetic, or we try and multiply everything out to eliminate the fractions :
15y + 30/25 = 11
375y + 30 = 275
375y = 245
y = 245/375 = 49/75
the same result, of course, but a slightly different way to get there.
Find all the cube roots of
[tex]z = 2e {}^{i\pi} [/tex]
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Answer:
{∛2e^(iπ), ∛2·e^(iπ/3), ∛2·e^(-iπ/3)}
Step-by-step explanation:
[tex]\displaystyle \sqrt[3]{z}=(2e^{i\pi})^{\frac{1}{3}}=(2e^{i(2n+1)\pi})^{\frac{1}{3}}=\sqrt[3]{2}\cdot e^{i(2n+1)\pi/3}\quad\text{for $n=\{-1,0,1\}$}\\\\=\{\sqrt[3]{2}\cdot e^{-i\pi/3},\sqrt[3]{2}\cdot e^{i\pi/3},\sqrt[3]{2}\cdot e^{i\pi}\}[/tex]
__
Additional comment
z = -2. ∛z will be three points in the complex plane on a circle of radius ∛2 at angles ±π/3 and π radians (±60° and 180°). That is, the real cube root of -2 is -∛2.
∆RMQ ≅∆RMS by __________ congruence criterion
SAS
SSA
AAS
SSS
[tex] \huge \pink{ \underbrace { \overbrace { \ SAS}}}[/tex]
Select the correct answer. Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3? A.It is the graph of f(x) translated 3 units down. B.It is the graph of f(x) translated 3 units to the left. C.It is the graph of f(x) where the slope is decreased by 3. D. It is the graph of f(x) translated 3 units up.
Answer: Choice A) translated 3 units down
Explanation:
x is the input while y = f(x) is the output. If we say f(x) - 3, then it's the same as saying y - 3. This means g(x) = f(x) - 3 subtracts 3 from each y coordinate of the points on f(x). This visually moves the entire f(x) curve down 3 units
Enter the correct answer in the box.
Linear function is shown in the graph. Write the slope-intercept form of the equation representing this function.
Y
10
8
6-
4
2
-75
-8
-6
X
- 5
-4
O
4
6
8
10
-2-
-4
-6-
N
-84
Answer:
Slope = 3
y-intercept: - 7
y = 3x -7
Step-by-step explanation:
What is the volume of a square pyramid that is 15cm tall and has a base area of 16 square centimeters
Answer:
Formula
V=a^2h/3
a is the base area
h is the height
V= 16^2×15/3
V=1280cm^3
Select the matrix multiplication that transforms vector A to
vector B
Answer:
Option C.
Step-by-step explanation:
Notice that only option B and C involves the vectors in transformation
[tex]A=\begin{bmatrix}4\\2\end{bmatrix}, B=\begin{bmatrix}-8\\-4\end{bmatrix}[/tex]
However, option B is not a defined multification since the dimension of both matrices are not matching. Vector A is 2x1 but the second matrix is 2x2.
WILL MARK BRAINIEST IF FAST!
Kane's Furniture Store advertised a table at a 11% discount. The original selling price was $111, and the sale price was $100. Was the sale price consistent with the ad? Explain.
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O A. No, the sale price was s higher than it should have been
(Round to the nearest cent.)
OB. No, the sale price was $ lower than it should have been
(Round to the nearest cent.)
OC. Yes, the sale price was consistent with the ad, because it represents a 11% discount.
va
Vi
(11)
More
Click to select and enter your answer(s) and then click Check Answer.
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Check
Answer:
A. No, the sale price was 1.21 higher than it should have been
Step-by-step explanation:
First find the discount
111 * 11%
111 * .11
12.21
Subtract this from 111
111-12.21
98.79
The sale price should have been 98.79
100-98.79
1.21
help me now where are you all helppppp
Q7
7/25
(Decimal: 0.28)
Step-by-step explanation:
Here's the little secret you can use to instantly transform any fraction to a decimal: Simply divide the numerator by the denominator:
= 7/25
= 7 ÷ 25
= 0.28
In Evan's math class, there are 7 boys and 10 girls. Which of the following is the ratio of boys to girls in Evan's math class?
Answer:
7/17
Step-by-step explanation:
What is 10% Compound interest of R15 000 every month for 3 years?
Answer:
19500
Step-by-step explanation:
30/100 X 15000 = 4500
15000 + 4500 = 19500
Answer:
A = $19,965.00
A = P + I where
P (principal) = $15,000.00
I (interest) = $4,965.00
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 15,000.00(1 + 0.1/1)(1)(3)
A = 15,000.00(1 + 0.1)(3)
A = $19,965.00
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $15,000.00 at a rate of 10% per year compounded 1 times per year over 3 years is $19,965.00.
1. Dorothy was able to answer yes to 16/25 of the survey questions. What is 16/25
written as a decimal?
Answer:
16/25 as a decimal is 0.64
Step-by-step explanation:
Vito avido is a sales representative for a company that sells roofing material. he receives a graduated commission of 5 percent on the first $5,000 of sales, 6.5 percent on the next $15,000, and a 7 percent on sales over $20,000. What is his commission on $23,458 in sales?
Hence commission will be 7%
[tex]\\ \rm\longmapsto 23458\times \dfrac{7}{100}[/tex]
[tex]\\ \rm\longmapsto \dfrac{164206}{100}[/tex]
[tex]\\ \rm\longmapsto 1642.06[/tex]
Vito Avido's commission on $23,458 in sales is $1466.06.
Here, we have to calculate Vito Avido's commission on $23,458 in sales, we'll break down the sales amount into different ranges and apply the respective commission rates for each range.
For the first $5,000 of sales: 5% commission
Commission = 5% of $5,000 = 0.05 * $5,000 = $250
For the next $15,000 of sales: 6.5% commission
Commission = 6.5% of $15,000 = 0.065 * $15,000 = $975
For the remaining amount over $20,000: 7% commission
Sales above $20,000 = $23,458 - $20,000 = $3,458
Commission = 7% of $3,458 = 0.07 * $3,458 = $241.06
Now, add up the commissions from each range:
Total Commission = $250 + $975 + $241.06 = $1466.06
Vito Avido's commission on $23,458 in sales is $1466.06.
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Which set of ordered pairs represents a function?
{(3,6), (3, 1), (9,0), (2, 2)}
{(2,-5), (-3, 6), (-1, -8), (-3,-4)}
{(4, -7), (-2, -1), (-7,4), (9, -1)}
{(3,8), (-2,-9), (1,4), (1,9)}
Answer:
{(4, -7), (-2, -1), (-7,4), (9, -1)}
Step-by-step explanation:
Every other set of ordered pairs has an x-value that has more than one y-value. This is against the rules of a function. Therefore, {(4, -7), (-2, -1), (-7,4), (9, -1)} represents a function.
Write 96% as a fraction.
Answer:
Directly, it would be 96/100. However, we can reduce it to become 48/50 = 24/25.
(underlined is simplest answer)
24/25
Step-by-step explanation:
96%
=96/100
=24/25
answer
The graph represents a function.
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (0,0)
0 (-3,1)
0 (1,3)
O (31)
If we consider the ordered pair (0,0) then only the graph still represents a function.
How to define a graph represent a function?
In a function, there can not be two different values of x corresponding to the same value of y.
Here, the points on the graph are (0,0), (-3,1), (1,3) and (3, 1).
If we consider point (-3,1) then there will be two points corresponding to the same y value i.e. (-3,1) and (3, 1).
The values of x for a single value of y.
i.e. y = 1.
So, if we consider the ordered pair (0,0) then only the graph still represents a function. Therefore, the correct answer is option (a) (0,0).
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