Answer: Let x=length of the longest side of the smaller triangle.
x/20=3/12
x=60/12
x=5
Final answer:
To find the longest side of the similar triangle, multiply the longest side of the original triangle (20) by the scale factor, which is the ratio of the shortest sides (3/12 = 0.25). This results in a longest side of 5 units for the similar triangle.
Explanation:
The question pertains to finding the longest side of a similar triangle given that the shortest side is 3 and the original triangle has sides 12, 15, and 20. To find the answer, we need to calculate the scale factor between the similar triangles. The scale factor is obtained by dividing the shortest side of the new triangle (3) by the shortest side of the original triangle (12), which is ¼ or 0.25.
We then multiply the longest side of the original triangle (20) by the scale factor (0.25) to get the longest side of the similar triangle. Calculating, 20 * 0.25 = 5. Therefore, the longest side of the triangle with the shortest side 3 is 5 units long.
Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 12 of a gallon of gas (g). Write an equation in the form of d=rg that represents the relationship between distance (d) and the number of gallons of gas (g), where r is the constant of proportionality.
Answer:
[tex]d =30g[/tex]
Step-by-step explanation:
Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 1/2 of a gallon of gas (g)
Distance d= 15
Gallons of gas (g)= 1/2
Equation is d= rg
Now plug in the values
15 = r* 1/2
Now we divide by 1/2 on both sides
[tex]r=\frac{15}{\frac{1}{2}}=15 * \frac{2}{1}= 30[/tex]
r=30
Now we replace the value of 'r' in the equation d=rg
[tex]d = 30g[/tex]
In an arithmetic series t6 = −4, t10 = −12. Find S10.
Answer:
[tex]S_{10}[/tex] = - 30
Step-by-step explanation:
For a given arithmetic sequence the n th term formula is
[tex]t_{n}[/tex] = [tex]t_{1}[/tex] + (n - 1)d
where d is the common difference and [tex]t_{1}[/tex] the first term
We have to find d and [tex]t_{1}[/tex]
from the given information we can write 2 equations and solve for d and [tex]t_{1}[/tex]
[tex]t_{6}[/tex] = [tex]t_{1}[/tex] + 5d = - 4 → (1)
[tex]t_{10}[/tex] = [tex]t_{1}[/tex] + 9d = - 12 → (2)
subtract (1) from (2) term by term
4d = - 8 ⇒ d = - 2
substitute d = - 2 in (1)
[tex]t_{1}[/tex] - 10 = - 4 ⇒ [tex]t_{1}[/tex] = - 4 + 10 = 6
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2[tex]t_{1}[/tex] + (n - 1)d ], hence
[tex]S_{10}[/tex] = 5[(2 × 6) + (9 × - 2) ] = 5(12 - 18) = 5 × - 6 = - 30
What are the vertical and horizontal asymptotes for the function 3x^2/x^2-4
Answer: vertical asymptotes: x = 2, x = -2
horizontal asyptote: y = 3
Step-by-step explanation:
[tex]\dfrac{3x^2}{x^2-4}[/tex]
Vertical Asymptotes are the restrictions on "x", which is denoted by the denominator being unequal to zero.
x² - 4 = 0
(x + 2)(x - 2) = 0
x + 2 = 0 and x - 2 = 0
x = -2 and x = -2
Horizontal Asymptotes are determined by the degree of the numerator (n) compared to the degree of the denominator (m) as follows:
If n > m , then no horizontal asymptote (use long division to find slant asymptote)If n = m , then horizontal asymptote is coefficient of n divided by coefficient of mIf n < m , then horizontal asymptote is: y = 0In the given problem, the degree of both the numerator and denominator is 2 so horizontal asymptote is: [tex]y = \dfrac{3}{1} = 3[/tex]
Find the sum of the geometrical equation -3 , 18 , -108 , if there are 7 terms
Hello from MrBillDoesMath!
Answer:
Sum = -119,962 ( I hope!)
Discussion:
Let's determine the pattern.
first term: -3
2nd term: (-3) * (-6) = 18 (multiply first term by -6)
3rd term: (18) * (-6) = -108 (multiply 2nd term by -6)
4th term : (-108)*(-6) = 648 ( etc)
5th term : (648)*(-6) = -3888 (etc)
6th term : (-3888)*(-6) = 23328 (etc)
7th term: (23328)*(-6) = -139967 (etc)
Sum = -119,962
A simpler way to do this is to use the formula for the sum of a geometric series to n terms. The series is
-3 Sum ( -6)^n n = 0, 1, 2, 3, 4, 5, 6
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
I need help with #7 ?!!!
Btw #6 is correct
Choice C for problem 6 is correct. The two angles (65 and 25) add to 90 degrees, proving they are complementary angles.
===========================================
The answer to problem 7 is also choice C and here's why
To find the midpoint, we add up the x coordinates and divide by 2. The two points A(-5,3) and B(3,3) have x coordinates of -5 and 3 respectively. They add to -5+3 = -2 which cuts in half to get -1. This means C has to be the answer as it's the only choice with x = -1 as an x coordinate.
Let's keep going to find the y coordinate of the midpoint. The points A(-5,3) and B(3,3) have y coordinates of y = 3 and y = 3, they add to 3+3 = 6 which cuts in half to get 3. The midpoint has the same y coordinate as the other two points
So that is why the midpoint is (-1,3)
how to find plato algebra 1 answers
To find Plato's Algebra 1 answers, it's important to understand the principles of algebra, apply them to solve problems, and practice regularly. Seek help from tutors, textbooks, and online resources, and strive to understand the process, not just find the answers.
Explanation:Finding answers to Plato's Algebra involves understanding the concepts and principles of Algebra, applying these to solve problems, and continuously practising. Consider seeking help from your teacher, using textbooks, online resources, and practicing more problems. Whatever resources you use, it's crucial to check your answers with a credible source. Remember, the goal is not only to find the answers but to understand how to solve different algebraic problems.
In Algebra 1, you will come across different topics such as equations, inequalities, functions, and graphing. Each topic requires understanding the fundamental concepts and practising the exercises.
For example, if you're solving a linear equation, it's important to know that what you do on one side of the = sign has to be done on the other side to maintain balance. With lots of practice, Algebra 1 will become easier to grasp.
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Evaluate the expression: (–2)2 + (–42) + (18 – 23).
A. –19
B. 19
C. –17
D. 3
Answer:
The correct answer is for the given expression is -43.
Step-by-step explanation:
We are given the following expression and we are supposed to evaluate it:
[tex](-2)^2 + (-42) + (18 - 23)[/tex]
Solving the terms inside the brackets first, following the order of operations to solve a mathematical expression to get:
= 4 + (-42) + (-5)
Further adding and subtracting the terms to get:
= 4 - 42 - 5
= -38 - 5
= -43
Answer:
-17
Step-by-step explanation:
Evaluate the expression: (–2)^2 + (–4^2) + (18 – 23) = -17
In which equation is the constant of proportionality 5?
a. x = 5y
b. y = 5x
c. 6 = x + 5
d. 6 = 5 - x
a door frame is 80 inches tall and 36 inches wide, what is the length of diagonal of the door frame? round to the nearest 10th
To find the diagonal of a door frame, use the Pythagorean theorem. Substitute the door's height and width into the formula, then find the square root of the sum. Round your answer to the nearest tenth.
Explanation:To find the length of the diagonal of the door frame, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the long side, or in this case, the diagonal) is equal to the sum of the squares of the other two sides (height and width of the door).
So, the formula becomes: Diagonal = √((Height)^2 + (Width)^2)
Substitute the given values of the height and width into the equation: Diagonal = √((80 inches)^2 + (36 inches)^2) = √(6400 + 1296) = √7696
The square root of 7696 is about 87.7 inches. So, the length of the diagonal of the door frame, rounded to the nearest tenth, is 87.7 inches.
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To calculate the length of the diagonal of the door frame, use the Pythagorean theorem by squaring the width and height, adding the squared values, and then taking the square root. The length of the diagonal is approximately 87.9 inches.
Explanation:To calculate the length of the diagonal of the door frame, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the width and the height of the door frame form the legs of the right triangle, and the diagonal is the hypotenuse. Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
Therefore, the length of the diagonal of the door frame is approximately 87.9 inches, rounded to the nearest 10th.
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Mindy opens a bank account with $55 and start saving five dollars per week. Sean’s grandma gives him $100 for his birthday, but he spends $10 every week. After how many weeks would they have the same amount of money, how much will that be?
Answer:
3 weeks, $45
Step-by-step explanation:
So we can make an equation!
55+5x=100-10x
So solving for x,
X=3
Final answer:
After solving the equations, Mindy and Sean will have the same amount of money, which is $70, after 3 weeks.
Explanation:
The question is about finding after how many weeks Mindy and Sean would have the same amount of money and how much that amount would be. Let's denote the number of weeks as w. For Mindy, who starts with $55 and saves $5 per week, her amount of money as a function of weeks is 55 + 5w. For Sean, who starts with $100 and spends $10 every week, his amount of money as a function of weeks is 100 - 10w.
To find out after how many weeks they would have the same amount of money, set the two expressions equal to each other:
55 + 5w = 100 - 10w
Add 10w to both sides and subtract 55 from both sides to solve for w:
15w = 45
Therefore, w = 45 / 15 = 3
To find out how much money they would have, substitute w = 3 into one of the original equations:
Mindy: 55 + 5(3) = 70
So, after 3 weeks, both Mindy and Sean will have $70
On Monday,it took Helen 3 hours to do a page of science homework exercises.The next day she did the same number of exercises in 2 hours. If her average rate on Monday was p exercises per hour what was her average rate the next day .In terms of p?
Answer:
It's 3/2p!
Step-by-step explanation:
Because Helen do the same number of exercises on 2 days, the time to do and the average rate are inversely proportional!
So, if on Monday, Helen's average rate is p then on the next day, her average rate is:
p × 3 ÷ 2 = [tex]\frac{3p}{2}[/tex]
=3/2p
Brainliest?
which has less water a swimming pool that is 5/10 full or a glass that is 9/10 full
Answer: A swimming pool that is 5/10 full.
Please help. Due today.
Answer: Try checking B
Step-by-step explanation:
Answer: lower right hand corner
In this corner is an expression that has "pi" in it that doesn't cancel out like it does in the upper left hand corner. The number pi is irrational because it cannot be written as a fraction of two whole numbers. We can sorta get close when we say 22/7 = 3.14129 but the more accurate version of pi is pi = 3.14159; however we cannot get an exact match.
How do you solve:
3(a+2)=2(a-7) and 9(t-1)=6(t+2)-t
Answer:
t=3
Step-by-step explanation:
Simplifying
5 + -1(t + 3) = -1 + 2(t + -3) Reorder the terms:
5 + -1(3 + t) = -1 + 2(t + -3)
5 + (3 * -1 + t * -1) = -1 + 2(t + -3)
5 + (-3 + -1t) = -1 + 2(t + -3)
Combine like terms: 5 + -3 = 2
2 + -1t = -1 + 2(t + -3)
Reorder the terms:
2 + -1t = -1 + 2(-3 + t)
2 + -1t = -1 + (-3 * 2 + t * 2)
2 + -1t = -1 + (-6 + 2t)
Combine like terms: -1 + -6 = -7
2 + -1t = -7 + 2t
Solving
2 + -1t = -7 + 2t
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '-2t' to each side of the equation.
2 + -1t + -2t = -7 + 2t + -2t
Combine like terms: -1t + -2t = -3t
2 + -3t = -7 + 2t + -2t
Combine like terms: 2t + -2t = 0
2 + -3t = -7 + 0
2 + -3t = -7
Add '-2' to each side of the equation.
2 + -2 + -3t = -7 + -2
Combine like terms: 2 + -2 = 0
0 + -3t = -7 + -2
-3t = -7 + -2
Combine like terms: -7 + -2 = -9
-3t = -9
Divide each side by '-3'.
t = 3
Simplifying
t = 3
how to factorised quadratics
in simple form thank you
Answer:
ax²+ bx + c = 0
Step-by-step explanation
Multiplying (x+4) and (x−1) together (called Expanding) gets x2 + 3x − 4 :
expand vs factor quadratic
So (x+4) and (x−1) are factors of x2 + 3x − 4
Just to be sure, let us check:
(x+4)(x−1) = x(x−1) + 4(x−1)
= x2 − x + 4x − 4
= x2 + 3x − 4 yes
Yes, (x+4) and (x−1) are definitely factors of x2 + 3x − 4
To factorise a quadratic equation, express it in the standard form ax² + bx + c = 0, identify coefficients a, b, and c, and then apply the quadratic formula.
To factorise quadratics in their simplest form, you need to express them in the standard quadratic form, which is ax² + bx + c = 0. For example, if you are given the equation x² + 4x - 21 = 0, you should identify a = 1, b = 4, and c = -21. Then you can apply the quadratic formula:
'x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c’, all over two 'a' (x = [tex]\frac{-b \pm \sqrt{b^2- 4ac} }{2a}[/tex])
If you are given an equation like 3x +3 + x² + x = 24, first rearrange it into the standard quadratic form by combining like terms. Use the quadratic formula if you cannot factor the quadratic easily.
Keep in mind that the quadratic formula can only be used if the equation is a true quadratic with powers confined to the second, first, and zeroth (constant term). If other powers or roots are present, then alternative methods must be used.
The product of two numbers is 48 and one of the numbers is 12 what is the other number
Answer:
4
Step-by-step explanation:
What graph represents the system of linear inequalities? 4x+y>1 y≤32x+2
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]4x+y>1[/tex] -----> inequality A
The solution of the inequality A is the shaded area above the dashed line
The equation of the dashed line is [tex]4x+y=1[/tex]
The slope of the dashed line is negative
The y-intercept of the dashed line is the point [tex](0,1)[/tex]
The x-intercept of the dashed line is the point [tex](0.25,0)[/tex]
[tex]y\leq \frac{3}{2}x+2[/tex] -----> inequality B
The solution of the inequality B is the shaded area below the solid line
The equation of the solid line is [tex]y=\frac{3}{2}x+2[/tex]
The slope of the solid line is positive
The y-intercept of the solid line is the point [tex](0,2)[/tex]
The x-intercept of the solid line is the point [tex](-1.33,0)[/tex]
using a graphing tool
The graph in the attached figure
Find the number if: 4% of it is 31% of 16.4
Answer:
The number (x) is 127.1
Step-by-step explanation:
4% of a number (x) is equal to;
31% of 16.4
i.e 0.04x = 5.084
x = [tex]\frac{5.084}{0.04}[/tex] = 127.1
The number (x) is 127.1
Answer:
x = 127.1
Step-by-step explanation:
Let x be the unknown number.
It is given that 4% of the number is 31% of 16.4
4% of x = 31% of 16.4
[tex]x\times \dfrac{4}{100}=16.4\times \dfrac{31}{100}[/tex]
[tex]\dfrac{4x}{100}=\dfrac{508.4}{100}[/tex]
Multiply both sides by 100.
[tex]\dfrac{4x}{100}\times 100=\dfrac{508.4}{100}\times 100[/tex]
[tex]4x=508.4[/tex]
Divide both sides by 4.
[tex]x=\dfrac{508.4}{4}[/tex]
[tex]x=127.1[/tex]
Therefore, the unknown number is 127.1.
Triangles △GJI and △PKH are similar, and m∠G+m∠P=50°, and m∠I=48°. What are the measures of all the angles of these triangles ?
If ΔGJI and ΔPKH are similar, then ∡G≅∡P, ∡J≅∡K and ∡I≅∡H.
We have m∡G + m∡P = 50°, therefore m∡G = m∡P = 50° : 2 = 25°.
m∡I = 48° therefore m∡H = 48°.
We know, the sum of the measures of the angles of a triangle is equal 180°.
Therefore we have the equation:
m∡G + m∡J + m∡I = 180°
25° + m∡J + 48° =180°
73° + m∡J = 180° subtract 73° from both sides
m∡J = 107° → m∡K = 107°.
Answer: ΔGJI and ΔPKH: 25°, 107°, 48°The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex] and this can be determined by using the properties of the triangle.
Given :
Triangles △GJI and △PKH are similar.m∠G + m∠P = 50°, and m∠I = 48°.Given that triangle GJI and triangle PKH are similar therefore:
[tex]\rm \angle G = \angle P[/tex]
[tex]\rm \angle J = \angle K[/tex]
[tex]\rm \angle I = \angle H[/tex]
The sum of the interior angles of the triangle is [tex]180^\circ[/tex].
[tex]\rm \angle G + \angle I + \angle J = 180^\circ[/tex]
[tex]\rm 25^\circ + 48^\circ + \angle J = 180^\circ[/tex]
[tex]\rm 73^\circ + \angle J = 180^\circ[/tex]
[tex]\rm \angle J = 107^\circ = \angle K[/tex]
The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex].
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Drea and Sajini both worked at a local ice cream shop over the summer. Together, they earned a total of $425. Drea earned $25 more than Sajini. Write a system of two equations with two variables to model this problem. Use an algebraic method (substitution or linear combination) to solve the system. Graph both equations. Be sure to include the solution on your graph. How much did each person earn?
ps i can graph it myself i guess i just need the rest
Answer:
The money earned by Drea was [tex]\$225[/tex]
The money earned by Sajini was [tex]\$200[/tex]
Step-by-step explanation:
Let
x------> money earned by Drea
y------> money earned by Sajini
we know that
[tex]x+y=425[/tex] -----> equation A
[tex]x=y+25[/tex] ----> equation B
substitute equation B in equation A
[tex](y+25)+y=425[/tex]
solve for y
[tex]2y=425-25[/tex]
[tex]y=400/2=\$200[/tex]
Find the value of x
[tex]x=y+25[/tex] ----> [tex]x=200+25=\$225[/tex]
using a graphing tool
solve the system of equations
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is [tex](225,200)[/tex]
see the attached figure
Answer:
Drea: $225
Sajini: $200
Step-by-step explanation:
D + S = 425
D = S + 25
S + 25 + S = 425
2S = 400
S = 200
D = 200 + 25 = 225
A baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop. How many scoops will she need for the recipe?
Answer:
Step-by-step explanation:
8
She will need 8 scoops for the recipe if the baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
A baker has 2 2/3 cups of flour for her recipe
2 2/3 = 8/3
She only has a 1/3 cup scoop.
Scoops she will need for the recipe = (8/3)/(1/3) = 8
Thus, she will need 8 scoops for the recipe if the baker has 2 2/3 cups of flour for her recipe, but she only has a 1/3 cup scoop.
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An airplane can ascend at a rate of 52 1/2 meters in 2/3 of a second how many meters can the airplane ascend in one second.
A. 34 1/3
B. 39
C. 51 1/2
D. 77 1/4
omg it was wrong help!!!!!
Answer:
b is 63, not -63
Step-by-step explanation:
Answer:
-2 degrees per hour
-63 m
Step-by-step explanation:
Cooled means the temperature is decreasing
-14 degrees/7 hours
-2 degrees per hour
The total change in elevation will be a negative number
(-3*21) =
-63 m
im sorry this is math not mathimatics but what is 3 dived by 563? use paper and pencil to find quotient and remainder
Answer:
0.0053285968
Step-by-step explanation:
i am not srry
Answer:
187 r 2
Step-by-step explanation:
563/3
3 into 5=1 r 2
bring down the 2
3 into 26= 8 r 2
bring down the 2
3 into 23=7 r 2
What do you need to know?
Answer:
Math
Step-by-step explanation:
Answer:
D. 51%
Step-by-step explanation:
A store is offering a 20% discount on all sales over $50.if you purchase a shirt and a pair of jeans for $62.50,what is the amount of the discount you would receive
Answer:
50 dollars
Step-by-step explanation:
If you have a 20% discount,that means you pay for 80% of your items. So to find percent you make 80 percent 0.8 and then multiply by 62.50.
Answer:
$10
Step-by-step explanation:
You would multiply $62.50 by 20% or .2 to find the discount which is $10. If you need to find the sale price you would subtract $62.50 - $10 = $52.50.
Your discount amount is $10
Your Sale Price is $52.50
PLEASE HELP ME ASAP!!!!
Answer:
y= 5x + 3
Step-by-step explanation:
This is because you solve for slope, which is 5, then plug that into point slope form to get:
y - 8 = 5(x - 1)
y - 8 = 5x - 5
y = 5x + 3.
Answer:
y = 5x + 3
Step-by-step explanation:
Step 1. Find the slope
Each time x increases by 1 unit, y increases by 5 units.
m = slope = 5/1 = 5
Step 2. Find the y-intercept.
y = mx + b
When x = 4, y = 23.
23 = 5×4 + b
23 = 20 +b
b = 3
y = 5x + 3
The graph is a straight line with slope m = 5 and a y-intercept at y = 3.
A jar of 50 sour ball candies contains only 3 flavors. If there are 18 orange, 12 lemon, and 20 cherry sour balls, what is the probability that a randomly selected sour ball will be lemon or cherry? A. 3/125 B. 12/ 125 C. 16/25
Please show solution. Thanks in advance!
Option B. 12/ 125 is the answer.
Explanation
Total umber of sour ball candies = 50
Number of lemon candies = 12
Hence the probability to get a lemon candy is = 12/50
Number of cherry sour balls = 20
So, the probability to get a cherry sour ball = 20/50
So, to get the joint probability for a random selection to either get a lemon or cherry candy, we will multiply both the probabilities.
[tex]\frac{12}{50}*\frac{20}{50}[/tex]
= [tex]\frac{12}{125}[/tex]
Write Y=x^2+18x+90 In vertex form
Answer:
y = (x + 9)² + 9
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a parabola in standard form : ax² + bx + c : a ≠ 0
the the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² + 18x + 90 is in standard form
with a = 1, b= 18 and c = 90
[tex]x_{vertex}[/tex] = - [tex]\frac{18}{2}[/tex] = - 9
to find the corresponding y-coordinate substitute x = - 9 into the equation
y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9
⇒ y = (x + 9)² + 9 ← in vertex form
Solve algebraically please URGENT
y=5x−7
−6x−4y=−24
[tex]\left\{\begin{array}{ccc}y=5x-7\\-6x-4y=-24&\text{divide both sides by (-2)}\end{array}\right\\\left\{\begin{array}{ccc}y=5x-7&(*)\\3x+2y=12&(**)\end{array}\right\\\\\text{substitute }\ (*)\ \text{to}\ (**):\\\\3x+2(5x-7)=12\qquad\text{use distributive property}\\\\3x+(2)(5x)+(2)(-7)=12\\\\3x+10x-14=12\qquad\text{add 14 to both sides}\\\\13x=26\qquad\text{divide oth sides by 13}\\\\\boxed{x=2}\\\\\text{Put the vaalue of x to}\ (*):\\\\y=5(2)-7\\\\y=10-7\\\\\boxed{y=3}\\\\Answer:\ \boxed{x=2\ and\ y=3\to(2,\ 3)}[/tex]