Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{24+x}\\ a=\stackrel{adjacent}{24}\\ b=\stackrel{opposite}{32}\\ \end{cases}\implies (24+x)^2~~ = ~~24^2+32^2 \\\\\\ (24+x)(24+x)~~ = ~~24^2+32^2\implies \stackrel{F~O~I~L}{24^2+48x+x^2}~~ = ~~24^2+32^2 \\\\\\ 48x+x^2=32^2\implies x^2+48x-32^2=0\implies x^2+48x-1024=0 \\\\\\ (x-16)(x+64)=0\implies x= \begin{cases} 16~~\textit{\Large \checkmark}\\\\ -64 \end{cases}[/tex]
notice, we didn't use -64, since the value of "x" must be a positive value.
Find the exact value or type
"undefined"
tan(-315)
[?]
Answer:
the exact value of tan(-315) is 1
Answer:
The tangent of -315 is opp/adj = 1/1 = 1
Step-by-step explanation:
The angle -315 is in the 1st quadrant, in which we see a 45-45-90 triangle. Thus, this triangle has 'opposite side' = 1, 'adjacent side' = 1, and hypotenuse √2. The tangent of -315 is thus opp/adj = 1/1 = 1
Leslie’s puppy has 4 toys. Her cat has 36 toys.How many times more toys does the cat have than the puppy?
A.6
B.7
C8
D.9
This figure is the pre-image of a prism that has undergone a dilation with a scale factor of 3/4.
What is the surface area of the image after the dilation?
185 5/8 m²
219 3/8 m²
247 1/2 m²
292 1/2 m²
The surface area of the image after the dilation is 219 3/8 m²
What is an area?Area is the amount of space occupied by a two dimensional shape or object.
The surface area of the prism = 2(0.5 * 5 * 12) + (5 * 11) + (11 * 12) + (13 * 11) = 390 m²
The surface area of the image after the dilation = scale factor² * 390 m² = (3/4)² * 390 m² = 219 3/8 m²
The surface area of the image after the dilation is 219 3/8 m²
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-77x - 78x = -155x
-66y - (-66y) = -66y + 66y = 0
264 - (-666) = 264 + 666 = 930
This leaves us with -155x = 930. Dividing by -155 on both sides, we find:
x = -6
Substitute x = -6 into one of the two original equations, solve for y, and then state the full solution to the system of equations.
Answer:
I don't understand
Step-by-step explanation:
You answer it.
The volume of this right trapezoidal prism is 464.75 ft³.
What is the height, x, of the prism?
Enter your answer as a decimal in the box.
Answer:
so first you want to mulitply the 5,5,5.8, and 8 together to get 1160 then take away 464 from 1160 to get 696. then you add all of the numbers up to get 719.8 ten subtract .75 from that and you get 719.05. then take the cubic feet and get 200 then taky away 200 from 719.05 and get 519.05 then do that again
Step-by-step explanation:
219.05
What will be the angle A?
Answer: 30 degrees
Step-by-step explanation:
has parallel sides but is not a trapezoid
Answer:
Parallelogram
Step-by-step explanation:
Instead of one pair of parallel sides like in a trapezoid, a parallelogram has two pairs of opposite sides (for example a rectangle)
Based on a survey, assume that 35% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when six consumers are randomly selected,
delivery by drones. Identify the values of n, ×, p, and q.
Answer:
Suppose that we want to find the probability that when six consumers are randomly selected, actually three of them are comfortable with delivery by drones.
Step-by-step explanation: hopes this helps you!
Write this ratio as a fraction in simplest form without any units six weeks to 18 days
Answer:
7/3
Step-by-step explanation:
To write the ratio with no units. we need to have both parts of the ratio in the same units. That way the units cancel.
__
6 weeks : 18 days = (6×7) days : (6×3) days = 7 : 3
The ratio as a fraction is ...
(6 weeks)/(18 days) = 7/3
Need help with this geometric question ASAP, Thank you
a right triangle with a long leg (x+7) and a short leg with (x) and the hypothenuse is 13
Answer:
Area is 30cm^2 if thats what your asking
Step-by-step explanation:
Answer:
X = 5
Step-by-step explanation:
You need to use the Pythagorean theory to solve this question.
[tex] {13}^{2} = {x}^{2} + {(x + 7)}^{2} [/tex]
[tex]169 = {x}^{2} + ( {x}^{2} + 14x + 49)[/tex]
[tex]169 = 2 {x}^{2} + 14x + 49[/tex]
[tex]0 = 2 {x}^{2} + 14x + 49 - 169[/tex]
[tex]0 = 2 {x}^{2} + 14x - 120[/tex]
Now simply the equation by dividing everything by 2.
[tex]0 = {x}^{2} + 7x - 60[/tex]
[tex]0 = (x - 5)(x + 12)[/tex]
Now, you can find the possible solutions by setting each bracket to 0.
[tex]0 = x - 5[/tex]
[tex]5 = x[/tex]
OR
[tex]0 = x + 12[/tex]
[tex] - 12 = x[/tex]
However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.
11. Angles 1 and 2 are supplementary. Angle 2 is 1/3 the size of angle 1. What
are the degree measurements of each angle?
⚫️67.50 and 22.5°
⚫️22.5° and 90°
⚫️60 and 120°
⚫️135° and 45°
Answer:
90 for choice 1, 112.5 is for choice 2, 180 for choice 3, and 180 for choice 4.
Step-by-step explanation:
67.50 and 22.5 is a complementary angle because it adds up to 90 degrees.
22.5 and 90 added is 112.5 which is an obtuse angle
60 and 120 added is a supplementary angle because 60 + 120 is 180
135 and 45 is also a supplementary angle because 135+45 = 180
Simplify (cosx)(tanx)(cscx)
[tex]❖\qquad\qquad\huge\underline{{\sf Answer}} \qquad \normalsize❖[/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \cos(x) \times \tan(x) \times \csc(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: \cancel{ \cos(x) }\times \dfrac{ \cancel{ \sin(x)} }{ \cancel{ \cos(x) }} \times \dfrac{1}{ \cancel{\sin(x)} } [/tex]
[tex]\qquad \sf \dashrightarrow \:1[/tex]
The equivalent value is 1
1. If Frank has 2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin does he have?
d=
q=
2. If Sam has 3 times as many dimes as quarters and they have a combined value of 330 cents, how many of each coin does he have?
d=
q=
Find x in circle O (The figure is not drawn to scale)
Answer:
20.5 degrees
Step-by-step explanation:
So when the arc is being made from two lines coming out from the center, the measure of the arc is the same as the angle of the lines.
So the measurement of 41 degrees for the arc is also the angle of line OB and line OC.
Now that center line is the diameter, which means it is 180 degrees
So you can find the angle of line OA and OB:
180 - 41 = 139
Then, to find x you need to recognize that OB and OA is actually the radius of the circle, which means they are the same length.
This makes it an isosceles triangle. So, the angle of OB and BA is the same as OB and BA. The measurement of all the angles in a truianbgle is 180 degrees, so to find the measurement of x, you need to subtract 139 from 180:
180-139 = 41
And then divide by two to find the remaining two angles:
41/2 = 20.5
and that is x :)
Factor 2x2 + 7x + 10x + 35 by grouping.
Answer:
(x+5)(2x+7)
Step-by-step explanation:
x(2x+7) + 5(2x+7)
(x+5)(2x+7)
I hope this helps!!
Solve the equation X=
Step-by-step explanation:
I think the answer is x=70
What can be divided into 6 and 4 without leaving a remainder?
Answer:
6,12,18,24,30,36,42,48,54,60... All of the numbers in this list can be divided by 6 with no remainder.
A natural number that has at least one factor other than 1 and itself.
Hope it helps!!!Brainliest pls!!!what decimal part of one dollar is two dimes
Answer: Tenths place.
Step-by-step explanation:
0.20
The 2 is part of the tenths place.
Answer:
$0.20
Step-by-step explanation:
1 penny = $0.01
1 nickel = $0.05
1 dime = $0.10
1 quarter = $0.25
Two dimes = $0.20
Or 1/4 of a dollar
Or 0.2 because you don't need to add a 0 at the end of .2 or the $ sign.
Data Analysis 7th grade math
Laura kept a record of the number of minutes she spent at the gym this week.
Day Minutes
Monday 60
Tuesday 70
Wednesday 62
Thursday ?
How many minutes should she spend at the gym on Thursday in order to average 65 minutes a day for four days.
________ Minutes
she spends 68 minutes at the gym on Thursday in order to average 65 minutes a day for four days.
What is Average?The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values. This measure of central tendency is usually referred to as the "average".
Granted, Laura recorded how long she spent at the gym each day this week.
Let "x" represent the time she spent working out on Thursday.
Since,
Average = (sum of values)/ count of values
Thus, in our case
Average = (60 +70 +62 +x)/4
average is 65 minutes a day for four days.
65 = 192 +x)/4
192 +x = 260
x = 260-192
x = 68
Therefore, she spends 68 minutes at the gym on Thursday in order to average 65 minutes a day for four days.
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please help, have to turn in in 30 mins
Please attach some form of question first, thank you!
Will mark YOU brainliest!!
Express the following phrase as a unit rate:
135 miles on 9 gallons of gas
Answer: 15 miles per gallon
Step-by-step explanation:
135 divided by 9
15 miles per gallon
rate:
[tex]\sf \dfrac{distance}{amount \ of \ oil}[/tex]
[tex]\rightarrow \dfrac{135}{9}[/tex]
[tex]\sf \rightarrow15 \ miles \ per \ gallon[/tex]
URGENT I NEED IT NOW PLEASE HELP ME!!!!
Show that 9.1 is not a solution of the equation n-6.4 = 2.61. Then find
the solution
Answer:
The solution is 9.01.
Step-by-step explanation:
To prove that 9.1 isn't the solution we have to plug 9.1 into the equation. By replacing n with 9.1 we get 2.7 which isn't equal to 2.61.
To find the solution we must add 6.4 to both sides of the equation.
How do I solve for y?
Answer:
Step-by-step explanation:
The angle containing y and 63 are vertically opposite. They are equal.
y + 23 = 63 Subtract 23 from both sides
y +23-23 = 63 - 23
Answer y = 40
Complete the inequality.
(-9/8)/(-2 3/4) ? 3/22
>
<
=
Answer:
(-3/8)/(-2 3/4) = 3/22
Step-by-step explanation:
Solve the following;
[tex]\frac{\left(-\frac{3}{8}\right)}{\left(-2\frac{3}{4}\right)}[/tex]
[tex]=\frac{\left(-\frac{3}{8}\right)}{\left(-\frac{11}{4}\right)}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}[/tex]
[tex]=\frac{\frac{3}{8}}{\frac{11}{4}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]=\frac{3\cdot \:4}{8\cdot \:11}[/tex]
[tex]\frac{3}{22}[/tex]
Thus, [tex]\frac{\left(-\frac{3}{8}\right)}{\left(-2\frac{3}{4}\right)}[/tex] = [tex]\frac{3}{22}[/tex]
~Learn with lenvy~
A cuple travels 420 miles to dr0p their dughter off at summer camp. The trip back has a short cut and is only 360 miles. And the gas mileage is 50% better
due to a lighter load. Write an expression for the total gas used and simplify.
The expression for the simplified total gas used is 1.43x.
How to write the expression of the total gaslet the gas used on the way to camp "x"
Then the gas used on the way back can be calculated as follows:
360 / 420 × 0.5 × x
To calculate the total fuel used, We need to add this to the 'x' used on the way.
Therefore,
total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x
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Which number is a common multiple of 2 and 4?
A) 14
B) 24
C) 26
D) 34
LAST QUESTION MORE POINTS!
Answer:
Step-by-step explanation:
c I think I did the math that’s what it leads to so yeah
The statement "7 is 21 less than 28" is interpreted 7 = 21 - 28.
it's interpreted as 28 - 21 = 7
Help picture below please
Answer:
tkm
Step-by-step explanation:
First T the middle k and at last m