Answer:
[tex]x=8,\:x=-3[/tex]
Step-by-step explanation:
[tex]x^2-5x-24=0\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-5,\:c=-24:\quad x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\left(-24\right)}}{2\cdot \:1}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=8,\:x=-3[/tex][tex]=\frac{5+\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}}{2\cdot \:1}\\5+\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}\\5+\sqrt{121}\\=\frac{5+\sqrt{121}}{2}\\=\frac{5+11}{2}\\=\frac{16}{2}\\=8\\\frac{-\left(-5\right)-\sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-24\right)}}{2\cdot \:1}\\=\frac{5-\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}}{2\cdot \:1}\\5-\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}\\\left(-5\right)^2\\=25\\4\cdot \:1\cdot \:24\\=96\\=5+\sqrt{25+96}\\[/tex]
[tex]\frac{5-\sqrt{121}}{2\cdot \:1}\\\frac{5-11}{2}\\=-\frac{6}{2}\\=-3\\[/tex]
M(angle)1 =. Degrees
Answer:
Angle [tex]m\angle 1 = 35^o[/tex]
Step-by-step explanation:
Our goal is to find appropriate symmetries within the given diagram, so we can use the property of the addition of internal angles of a triangle that render [tex]180^o[/tex].
So we start by drawing a line that goes through the center of the circle and also through the vertex of angle [tex]m\angle 1[/tex]. Please see the attached image to follow the procedure. In the image, the line is a fine black line that crosses the circle completely.
Now we draw the four radii that will define clearly the central angles of [tex]100^o[/tex] and [tex]30^o[/tex] that come as information.
Then we set our efforts to analyze the two triangles (one marked with green borders, and the other one marked with orange borders. Notice that the angle on the further right for the triangle with orange borders is in fact half of the angle [tex]m\angle 1[/tex] that we need to find, so we will work our way to determine the size of it and then multiply it by two.
We need to start though with the triangle with green borders because it has more information that we can derive.
Notice that this green triangle has a central angle equal to [tex]115^o[/tex], because it has to measure the same as 180 degrees minus half of the 100 degrees angle and minus half of the 30 degree angle in order to add to form the perfect plane angle of the circle's diameter:
[tex]180^o-50^o-15^o=115^o[/tex]
Now, notice as well that this green triangle is an isosceles triangle (has two equal sides (both equal to the radius of the circle), and therefore the angles opposite to them must be equal. We can find the measure of either such angles by using the property of additions of internal angles of a triangle to render [tex]180^o[/tex], subtracting from it the 115 degree angle we know, and dividing the result by two:
[tex]180^o-115^o=65^o[/tex]
half of this is [tex]32.5^o[/tex]
Now we use this angle, to find its supplementary angle, which would be the angle on top of the orange triangle:
[tex]180^o-32.5^o=147.5^o[/tex]
Now all we need is to use the property of addition of internal angles for the orange triangle (of which we currently know a 15 degree angle and a 147.5 degree angle) to find what half of angle [tex]m\angle 1[/tex] is:
[tex]180^o-147.5^o-15^o=17.5^o[/tex]
then angle [tex]m\angle 1[/tex] is twice this value: [tex]m\angle 1 = 35^o[/tex]
A bag contains purple marbles and blue marbles, 38 in total. The number of purple marbles is 5 more than 2 times the number of blue marbles. How many purple marbles are there?
Answer:
27 purple marbles
Step-by-step explanation:
purple marbles- pblue marbles- bEquations based on the given:
p= 2b +5 and p+b= 38
2b+5+b= 38 ⇒ 3b+5= 38 ⇒ 3b= 33 ⇒ b= 11p= 38-11= 27What is the slope of a line that is perpendicular to the line in the graph?
Answer:
1
Step-by-step explanation:
The line in the graph has a slope of -1. The slopes of lines that are perpendicular have a product of -1 so the answer is 1.
What is the perpendicular and parallel line of 8x + 5y=4
Answer:
Perpendicular: [tex]y = \frac{5}{8}x+4[/tex]
Parallel: [tex]y=-\frac{8}{5} x+RandomNumberNot4[/tex]
Step-by-step explanation:
I'm going to rewrite the equation:
[tex]y=-\frac{8}{5} x+\frac{4}{5}[/tex]
Perpendicular means that the slope is the opposite reciprocal.
Slope = [tex]\frac{5}{8}[/tex]
[tex]y = \frac{5}{8}x+4[/tex]
Parallel means that the slope is the same but the y - intercept is different:
[tex]y=-\frac{8}{5} x+RandomNumberNot4[/tex]
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!
Answer:
-8/3
Step-by-step explanation:
find slope
(-1,5) ( 2,-3 )
(-3 -5)/( 2-(-1)) = -8/3
Triangle EFG has vertices E(-3,4), F(-5,1), and G(1,1). The triangle is translated so that the coordinates of the image are E’(-1,0), F’(-3,-5), and G’(3,-3).
Answer:
first Horizontal translation right '2' units and vertical translation up '-4' units
E ( -3 +2 , 4+(-4)) → E¹(-1 ,0)
F(-5 +2 , -1 +(-4) → F¹(-3 ,-5)
G( 1+2 , 1+(-4) → G¹(3 ,-3))
Step-by-step explanation:
Explanation:-
Now we will applying below rules
Type of transformations change to co-ordinate point
vertical translation up 'd' units (x,y)→(x, y+d)
vertical translation down 'd' units (x,y)→(x, y-d)
Horizontal translation left 'C' units (x,y)→(x-c, y)
Horizontal translation right 'C' units (x,y)→(x+c, y)
Now we will apply rule is
first Horizontal translation right 'C' units and vertical translation up 'd' units
Given E( -3 ,4 ), F(-5 ,1) and G(1,1)
first Horizontal translation right '2' units and vertical translation up '-4' units
and it translated E ( -3 +2 , 4+(-4)) → E¹(-1 ,0)
F(-5 +2 , -1 +(-4) → F¹(-3 ,-5)
G( 1+2 , 1+(-4) → G¹(3 ,-3))
Answer:C, The answer is the third option
What is the scale factor of this dilation?
5
В
3
e
3
A
5
Answer:
A dilation stretches or shrinks the original figure. A description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane. If the scale factor is greater than 1, the image is an enlargement (a stretch).
18) A TV screen has a length of 15 inches.
The diagonal of the TV is 25 inches. What
is the width of the TV?
A) 400 inches
B) 40 inches
C) 20 inches D) 29.2 inches
Answer: 20 inches
Step-by-step explanation:
From the question, a television screen has a length of 15 inches while the diagonal of the TV is 25 inches. To calculate the width, we will use the hypoteneous rule.
Hypotenuse² = length² + width²
25² = 15² + width²
width² = 25² - 15²
width² = 625 - 225
width² = 400
width = ✓400
width = 20
The width of the TV is 20 inches.
Jeremy is driving to his friends house that is 60 miles away from his home the scale on Jeremy's map is 1 1/2 inches equivalent to 9 miles how far is it on the map from jeremys house to his friends?
Answer:
The distance between their house on the map is 10 inches.
Step-by-step explanation:
In order to calculate the distance from Jeremy's friend house to his we can apply a rule of three in a way that 60 miles is related to "x" inches in the same proportion as "1 1/2" inches is related to 9 miles. Before applying that it'll be for the best if we convert the mixed fraction to a pure fraction as shown below:
[tex]d = 1\frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}[/tex]
Creating the rule of three:
[tex]\frac{60}{9} \frac{\text{miles}}{\text{miles}} = \frac{x}{\frac{3}{2}} \frac{\text{inches}}{\text{inches}}\\\\9*x = \frac{60*3}{2}\\\\x = \frac{180}{18}\\\\x = 10 \text{ inches}[/tex]
The distance between their house on the map is 10 inches.
There are 40 nickels in a roll. If you have 250 rolls of nickels, how many nickels do you have? pls can someone help me?
Answer:
10,000 nickels
Step-by-step explanation:
PLEEEASE HELP!!! EXPLAIN ALL PARTS!!!
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
Answer:
see below
Step-by-step explanation:
A: Some points could be (1, 7.5), (2, 7), (3, 6.5), (4, 6), (5, 5.5) and (6, 5) because the y-coordinates all represent the heights of the candle after the x hours.
B: This is a function because no input has multiple outputs.
C: It would still be a function because no input would have multiple outputs.
Answer:
Have a great day!!
Step-by-step explanation:
Part A: my rate of change was first y= - 5x + 8 the reason i put a negative sign beforehand is that when the candle melts its height it's decreasing
(0,8),(1,7.5)(2,7)(3,6.5)(4,6)(5, 5.5)
Part B: This is a function because there is one different output for each different input
Part C: yes, it still would be a function because the numbers haven't changed and are exactly the same and it still has one input for each output.
(0,8), (1,75), (2,7), (3,6.5), (4,6), (5,5.5)
Write the equation in standard form: 3x + 1 = 2y
3x + 2y = 1
3x + 2y = –1
3x – 2y = –1
3x – 2y = 1
Answer:
3x+2y=-1
Step-by-step explanation:
moving the numbers around, the outcome will have to be different
// have a great day //
Answer:
c) 3x - 2y = -1
Step-by-step explanation:
Given equation,
→ 3x + 1 = 2y
Conversion into standard form,
→ 3x + 1 = 2y
→ 3x + 1 - 2y = 0
→ 3x - 2y = -1
Hence, option (c) is correct.
Allan built a doghouse and he wanted the house to have an area of 24 square feet. He also wanted the width to be 2/3 the length. What are the dimensions of the doghouse?
Answer:
Dimension of doghouse is 4ft by 6ft
Step-by-step explanation:
Here, we are interested in calculating the dimensions of the doghouse.
Let the length of the doghouse be x, this means that the width would be 2/3 of x which equals 2x/3
Now, the area of rectangle is L * B
x * 2x/3 = 24
2x^2 = 3 * 24
2x^2 = 72
diverse both sides by 2
x^2 = 36
hence x = 6ft
The width would be 2/3 * 6 = 12/3 = 4 ft
What common fraction must be added to 1/6 to equal 1/2(Working please)
Answer:
1/3
Step-by-step explanation:
let the common fraction be x
we get,
1/6 + x = 1/2
x = 1/2 - 1/6
x = 6 - 2/12
x = 4/12
x = 1/3
VERIFICATION:1/6 + x = 1/2
1/6 + 1/3 = 1/2
3 + 6/18 = 1/2
9/18 = 1/2
1/2 = 1/2
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
Answer:
Aaron;s rate for mowing lawns is 0.5 acres per hour."as1.5 acres / 3 hours = 0.5 acres an hour2.5 acres / 5 hours = 0.5 acres an hour Option (B)
Step-by-step explanation:Aaron;s rate for mowing lawns is 0.5 acres per hour."as1.5 acres / 3 hours = 0.5 acres an hour2.5 acres / 5 hours = 0.5 acres an hour
find the 7th term of the geometric progression which begins:
2, -6, 18...
Answer:
a7=1458
Step-by-step explanation:
2; -6; 18... a geometric progression
a1=2; a2=-6; a3=18
r=a2/a1=-6/2
r= -3
a7=a1*r⁶
a7=2*(-3)⁶=2*729
a7=1458
asif has a bag of 58 sweets he gives 5 of his sweets to each of his 6 friends how many sweets does he have left
Answer:28 if I’m not mistaken
Step-by-step explanation:
Please help me in this
Answer:
3
Step-by-step explanation:
as u add 2 + 1 from the 6 and 7 hours
what is the area of the circle?
Answer:
A = 90.25π
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
r = 9.5
A = 90.25π
Answer:
[tex]\pi \times 9.5 {?}^{2} [/tex]
If GF = 3.2 ft, which is a possible measure of T5?
1.6 ft
3.0 ft
3.2 ft
4.0 ft
Complete Question:
In the triangles, TR= GE and SR=FE. If GF= 3.2 ft, which is a possible measure of TS?
Answer:
3.2ft
Step-by-step Explanation:
From the given information of the question, we can draft out the diagram of the triangles being depicted here. See attached picture showing triangles RST and EFG.
Since we are told that TR= GE, and SR = FE, it means both triangles are isosceles triangle a having 2 equal sides, and triangles RST and EFG are similar.
Also, given that the measure of the 3rd side (GF) of triangle EFG is 3.2ft, therefore, TS = 3.2ft
Answer:
c
Step-by-step explanation:
There are two red jars of marbles and one blue jar of marbles. Jars of a certain color have the same number of marbles in them. There are 30 marbles in total. The difference between the number of marbles in a red jar and the number of marbles in a blue jar is 12. Find the number of marbles in each type of jar.
Answer:
There are 14 marbles in each red jar and 2 marbles in the blue jar
Step-by-step explanation:
There are two red jars of marbles and one blue jar of marbles.
Let the number of marbles in the red jar be x.
Let the number of marbles in the blue jar be y.
There are 30 marbles in total. This means that:
2x + y = 30 _____________ (1)
The difference between the number of marbles in a red jar and the number of marbles in a blue jar is 12. This means that:
x - y = 12 ______________(2)
We have a system of simultaneous equations:
2x + y = 30 _____________ (1)
x - y = 12 ______________(2)
Add them together:
3x = 42
=> x = 42/3= 14
Put the value of x in (2)
14 - y = 12
=> y = 14 - 12 = 2
Therefore, there are 14 marbles in each red jar and 2 marbles in the blue jar.
Which of the following is equal to the ratio of the circumference of a circle to its diameter?
Answer:
Im pretty sure its the 1st one
Step-by-step explanation:
Answer:
option 3 π
Step-by-step explanation:
Circumference = πd
Circumference : diameter = πd : d
= π : 1 = π
Pls select the correct answer
Answer:
B
Step-by-step explanation:
Rent paid by Julie = (1/3) of 3000
[tex]=\frac{1}{3}*3000\\\\=1*1000[/tex]
= £ 1000
Remaining amount after paying rent = 3000 - 1000 = £ 2000
Expenses : Savings = 7 : 3
Total part = 7 + 3 = 10
Saving part = 3/10
Amount saved = (3/10) of 2000
[tex]=\frac{3}{10}*2000\\\\=3*200[/tex]
= £ 600
Answer:
B
Step-by-step explanation:
one third of £3000 = £3000 ÷ 3 = £1000
£3000 - £1000 = £2000 ← amount left after paying rent
Add the parts of the ratio, 7 + 3 = 10 parts
Divide the amount left by 10 to find the value of one part of the ratio
£2000 ÷ 10 = £200 ← value of 1 part of the ratio, thus
3 × £200 = £600
Julie saves £600 each month
Determine the length of MN to the nearest tenth of a centimetre.
Select one or more:
a. 3.0 cm
b. 4.0 cm
c. 2.8 cm
d. 2.1 cm
Answer:
b. 4.0 cm
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the ratio of the adjacent side to the hypotenuse is given by the cosine of the angle:
Cos = Adjacent/Hypotenuse
cos(35°) = NL/NK
NL = NK·cos(35°)
__
Similarly, it reminds you that the ratio of the opposite side to the hypotenuse is given by the sine function:
Sin = Opposite/Hypotenuse
sin(53°) = NM/NL
NM = NL·sin(53°)
Substituting from the first triangle, we have ...
NM = NK·cos(35°)·sin(53°)
NM = (6.1 cm)(0.81915)(0.79864)
NM ≈ 3.991 cm
MN ≈ 4.0 cm
The scale on a map is 1 cm:60 km. How many kilometers are represented by 2.5 centimeters on the map?
120 kilometers
105 kilometers
135 kilometers
150 kilometers
Answer:
150 km
Step-by-step explanation:
The scale tells you what real distance corresponds to a distance in the drawing. 1 cm in the drawing means 60 km of real distance.
Since 2.5 cm is 2.5 times 1 cm, it represents 2.5 times 60 km of real distance.
2.5 * 60 km = 150 km
Another inequality question :( Can someone help pls??
Thanks :D
Answer:
[tex]y\geq x[/tex]
Step-by-step explanation:
Again, let us begin by finding the equation of the line
The y-intercept is 0 and the slope is 1, so the equation of this line would be [tex]y=x+0[/tex] or just [tex]y=x[/tex]
We can see that the shaded region is ABOVE the line, so we would use a greater than (>) sign.
This as the line is shaded in, we must also include that line in the inequality. This means that we will instead use the [tex]\geq[/tex] sign.
This means that our answer would be [tex]y\geq x[/tex]
Question below. I have attached it below. Please answer it and comment the answer.
Answer:
(a)1/10
(b)1/5
(c)4/5
hope it helps
Answer:
answer for A) 1/10
answer for B) 1/10
answer for C) 8/10 given that you consider the digit '1' present in 10. if not, 9/10 is the answer
The slope of line p is _, and the slope of line Q is _.
Answer:
From the graph, the slope of line p is 3 and the slope of line q is -3.
what is 5k+(-2k)-(-1)
Answer:
Brainliest goes to me!
Step-by-step explanation:
5k-2k+1
3k+1
Tracy has a cell phone plan that provides 250 free minutes each month for a flat rate of $29.
Answer:
250 minutes with the flat rate of $29.
[tex]x\leq 250[/tex]
x would be the number of minutes called.
[tex]x-250[/tex]
Tracy would be charged by $0.35 per minute.
[tex]f(x)=29\\ 0\leq x\leq 250[/tex]
[tex]f(x)=0.35(x-250)+29,\\250\leq x\leq ∞[/tex]