Answer:
50 miles
Step-by-step explanation:
20 multiplied by 2.5 = 50
Yo fam for me
45 = 3(x + 1)
Answer:
x = 14
Step-by-step explanation:
Solving equation3(x + 1) = 45
3*x + 3*1 = 45 {Distributive property used: a*(b+c) =(a*b) +(a*c)}
3x + 3 = 45
Subtract 3 from both sides
3x = 45 - 3
3x = 42
Divide both sides by 3
x = 42/3
[tex]\sf \boxed{\bf x = 14}[/tex]
PLEASE HELP WILL MARK BRAINLIEST
Complete the Proof Statements Reasons 1. ABCD is a given AC BD 2. AD BC 3. 4. AABC=ABAD 5 ZDAB=LCBA 6. 7. ABCD is a rectangle 1. 2. 3. 4. 5. 6. 7. Congruent supp. angles are right angles 8. Given: ABCD is a parallelogram AC = BD Prove: ABCD is a rectangle SSS Triangle Congruence Theorem mZDAB = 90° m/CBA = 90° Reflexive Property of Congruence ZDAB and ZCBA are supplementary Definition of Rectangle O B CPCTC If the quad is a both pairs of opposite sides are congruent Consecutive angles in a are supplementary AB = AB
1) ABCD is a parallelogram, [tex]\overline{AC} \cong \overline{BD}[/tex] (given)
2) [tex]\overline{AD} \cong \overline{BC}[/tex] (if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent)
3) [tex]\overline{AB} \cong \overline{AB}[/tex] (reflexive property of congruence)
4) [tex]\triangle ABC \cong \triangle BAD[/tex] (SSS Triangle Congruence Theorem)
5) [tex]\angle DAB \cong \angle CBA[/tex] (CPCTC)
6) [tex]\angle DAB[/tex] and [tex]\angle CBA[/tex] are supplementary (consecutive angles in a parallelogram are supplementary)
7) [tex]m\angle DAB=90^{\circ}, m\angle CBA=90^{\circ}[/tex] (congruent supplementary angles are right angles)
8) [tex]ABCD[/tex] is a rectangle (definition of rectangle)
All the missing statements with the respective reasons are given below.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Statement 1.
ABCD is a parallelogram,
AC ≅ BD
Reason: Given.
Statement 2.
AD ≅ BC
Reason: if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent.
Statement 3. AB ≅ AB
Reason: reflexive property of congruence.
Statement 4. ΔABC ≅ ΔBAD.
Reason: SSS Triangle Congruence Theorem
Statement 5. ∠DAB ≅ ∠CBA
Reason: CPCTC
Statement 6. ∠DAB and ∠CBA are supplementary
Reason: consecutive angles in a parallelogram are supplementary.
Statement 7. m∠DAB = 90° and m∠CBA = 90°
Reason: congruent supplementary angles are right angles.
Statement 8. ABCD is a rectangle.
Reason: definition of a rectangle.
Therefore, all the required points are given above.
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Find the area of the yellow region.
Round to the nearest tenth.
5ft
Answer: 9.3
I calculated the area of the square, then I calculated the area of the circle. Then I subtracted the two.
Answer:
5.3
Step-by-step explanation:
A square has equal sides
LXW=A
5x5= 25
diameter of the circle is 5 ft
D/2=R 5/2= 2.5
Area of a circle is [tex]\pi r^2[/tex] (Pi=3.14)
[tex]3.14 X (2.5)^2[/tex]= 3.14 x 6.25= 19.625.
Area of yellow region
Area of square - Area of circle.
25-19.625 = 5.375 rounded to nearest 10th is 5.3
Which of the following could be the center of a circle that includes the points (-5, 2) and (-3, 6)?
A. (0, 2)
B. (0, -2)
C. (2, 2)
D. (2, 1)
The center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)
How to determine the center of the circle?The points are given as:
(-5, 2) and (-3, 6)
The equation of a circle is represented as:
[tex](x -a)^2 + (y - b)^2 = r^2[/tex]
Where:
Points = (x,y)Center = (a,b)Radius = rSubstitute both points in the above equation
[tex](-5 + a)^2 + (2 - b)^2 = r^2[/tex]
[tex](- 3+ a)^2 + (6 - b)^2 = r^2[/tex]
The radii are equal.
So, we have:
[tex](-5 + a)^2 + (2 - b)^2 = (- 3+ a)^2 + (6 - b)^2[/tex]
Expand the equations
[tex]25 -10a + a^2 + 4 - 4b + b^2 = 9 - 6a + a^2 + 36 - 12b + b^2[/tex]
Evaluate the like terms
[tex]25 -10a + 4 - 4b = 9 - 6a + 36 - 12b[/tex]
Collect like terms
6a -10a - 4b + 12b = 9 + 36 - 25 - 4
Evaluate
-4a + 8b = 16
Divide through by - 4
a - 2b = -4
Next, we test the options:
Option (a) (a,b) = (0,2)
Substitute these values in the equation
0 - 2*2 = -4
Evaluate
-4 = -4
Both sides of the equation are the same
Hence, the center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)
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A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 86m long and 64m wide. Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer. 64m 86m
To solve this problem, we have to find the area of the semi circles and the area of the rectangle and add them up together.
The area of the field is equal to 8719.36m^2
Area of the FieldLet us start by finding the area of the rectangle.
Data;
width = 86mlength = 64mArea of a rectangle is given as
[tex]a = length * width \\a = 86 * 64\\a = 5504m^2\\[/tex]
The area of the rectangle is 5504m^2
Area of the semicircle
The formula of a semi circle is given as
[tex]A = \frac{1}{2} \pi r^2[/tex]
But since we have two semi circles here, we can simply multiply it by two and the formula becomes
[tex]A = 2 * \frac{1}{2} \pi r^2\\A = \pi r^2[/tex]
But in the question, we have the diameter of the semi circle as the length of the rectangle.
[tex]radius = \frac{diameter}{2} \\radius = \frac{64}{2} \\radius = 32m[/tex]
The radius of the semicircle is 32m
Area of the semicircle is
[tex]A = \pi r^2\\A = 3.14 * 32^2\\A = 3215.36m^2[/tex]
The area of the field is
[tex]area of field = 3215.36 + 5504\\area = 8719.36m^2[/tex]
The area of the field is equal to 8719.36m^2
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given h(x) = 7x^2 -45x + 12, find h(x) = 18. help!! please explain and show work.
The value of variable x of provided quadratic function at h(x) = 18 are 6.56 and -0.13. These points explain solution of the equation.
What is quadratic formula?Quadratic formula is the formula which is used to find the roots of a quadratic equation.The standard form of the quadratic equation is,
ax²+bx+c=0
For the above equation, the quadratic formula can be given as,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The equation of variable x is given as,
h(x) = 7x²-45x + 12,
The value of h(x) = 18 has to be found out. Put 18 on the place of h(x) in the above equation.
18 = 7x²-45x + 12
0= 7x²-45x + 12-18
0=7x²-45x -6
Find the roots of the equation using the quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\dfrac{-(-45)\pm\sqrt{(-45)^2-4(7)(-6)}}{2(-6)}\\x=6.56,-0.13[/tex]
Thus, the value of variable x of provided quadratic function at h(x) = 18 are 6.56 and -0.13. These points explain the solution of the equation.
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Diana has a tool box in the shape of a right rectangular prism. The volume of the tool box is 1.62 cubic feet. The height of the tool box is 0.75 feet, and the length is 1.8 feet. What is the width of Diana's tool box? Enter your answer as a decimal in the box. ft
Answer:
I think you just have to multiply 0.75 and 1.8 then divided with 1.62.
Step-by-step explanation:
0.75*1.8=a
1.62/a= answer?
Answer:
the answer in 1.2 i just took the unit test on K12
Simplify: [tex]\sqrt{\frac{144}{25} }[/tex].
Answer:
[tex]\frac{12}{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{\frac{144}{25}}=\frac{\sqrt{144}}{\sqrt{25}}=\frac{12}{5}[/tex]
Given term:
[tex]\sqrt{\dfrac{144}{25} }[/tex]
This term can also be written as;
[tex]\implies \sqrt{\huge\text{(}\dfrac{144}{25} \huge\text{)}}[/tex]
Clearly, we can see that 144 and 25 are perfect squares. Then,
[tex]\implies\sqrt{\huge\text{(}\dfrac{12^{2} }{5^{2} } \huge\text{)}}[/tex]
According to an exponent property, (a²/b²) = (a/b)². Then,
[tex]\implies\sqrt{\huge\text{(}\dfrac{12}{5} \huge\text{)}^{2} }[/tex]
Since 12/5 is being squared inside the root, we can remove the squared symbol and take out 12/5 from the root. Then we get;
[tex]\implies\sqrt{\huge\text{(}\dfrac{12}{5} \huge\text{)}^{2} } \ = \ \dfrac{12}{5} \ = \ \boxed{2.4}[/tex]
Therefore, the simplified term is 2.4.
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What is the probability of randomly selecting a bird
3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then, they have been leaving Planet X at a rate of 120 residents per year.
The following equation describes this situation:
\quad -120\cdot 3 = -360−120⋅3=−360minus, 120, dot, 3, equals, minus, 360
What does -360−360minus, 360 tell us?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
A total of 360360360 residents left Planet XXX in the past three years.
(Choice B)
B
360360360 residents left Planet XXX each year.
(Choice C)
C
None of the above
Answer:
A total of 360 residents left Planet X in the past 3 years.
Step-by-step explanation:
120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.
Answers
A total of 360 residents left Planet X in the past 3 years.
Step-by-step explanation:
120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.A total of 360 residents left Planet X in the past 3 years.
Calculate (C ∘ F) for the month
To calculate temperature (C ∘ F) Celsius to Fahrenheit for the month, use the following expression.
[tex]^oC=\dfrac{5}{9}(^oF-32)[/tex]How to convert Celsius to Fahrenheit?
Temperature is the way to express the hotness or coldness of a body or object surface. The scales of measuring temperature are:
Celsius FahrenheitKelvinTo convert Fahrenheit to Celsius, we use the following formula.
[tex]^oF=^oC\times\dfrac{9}{5}+32[/tex]
The formula to convert Celsius to Fahrenheit is
[tex]^oC=\dfrac{5}{9}(^oF-32)[/tex]
Now, there is no data given in the problem. Thus, the above formula for any data can be used to convert the unit of temperature measurement.
Hence, to calculate temperature (C ∘ F) Celsius to Fahrenheit for the month, use the following expression.
[tex]^oC=\dfrac{5}{9}(^oF-32)[/tex]
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help me please :( i need help
Answer:
B
Step-by-step explanation:
Use the expression PEMDAS
It helps to know what do to first
Parenthesis Exponent Multiply Divide Add Subtract
I need help with this problem please.
Answer:
D
Step-by-step explanation:
what is the anwer pls
Answer:
180 square yards
Step-by-step explanation:
there are 3 shapes that create the total area :
a large right-angled triangle to the right. its baseline is 16 yd. the left side is a bit complicated, we get to it.
a small middle rectangle with length 6 yd. it's width is 3 yd.
is area is 6×3 = 18 yd²
a large rectangle at the bottom left with length 11 yd and width 6yd.
its area is 11×6 = 66 yd²
now, how long is the left side of the triangle ? we need it as the height of the triangle to get the area
baseline × height / 2
we see that a part of the left side is 8 yd.
then the width of the middle rectangle is also a part of that left side : 3 yd.
and then we notice that the triangle goes a little bit below the top length side of the large rectangle. how much ? well the actual width of the large rectangle is 6 yd, but the side under the triangle says only 5 yd. so, the missing piece is 6-5 = 1 yd.
so, the full left side is
8 + 3 + 1 = 12 yd
and the area of the triangle is
16×12 / 2 = 16×6 = 96 yd²
so, the total area of the figure is
18 + 66 + 96 = 180 yd²
Can somebody please help me with this
Answer: 3
Step-by-step explanation:
The price of a tv was decreased by 20% to £1440. What was the price before the decrease?
Answer:
€7200
Step-by-step explanation:
20%---------1440
100%----------y
y= 100×1440/20
y= 144000/20
y= €7200
price before decrease= €7200
of the prism below is a
square with a circular hole in it.
Work out the volume of the prism.
Give your answer to 3 s.f.
5 cm
6 cm
The cross-section
13 cm
Answer:
704 cm³
Step-by-step explanation:
Things to understand :
The 3D figure removed by making a circular hole through the prism is a cylinder. The original shape was a rectangular prism.Volume of the prism is equal to the difference between the volume of the rectangular prism and cylinder.Solving :
Volume (prism) = Volume (rectangular prism) - Volume (cylinder)
Volume = LWH - πr²h
Volume = 5 x 13 x 13 - π x 3² x 5
Volume = 845 - π x 45
Volume = 845 - 141.3
Volume = 704 cm³
[tex] \boxed{\sf \: Answer : Volume \: of \: prism \: is \: 703.7 cm³}[/tex]
Step-by-step explanation:
Information about diagram- The diagram is a square prism with a circular hole in it.
Given:
length of prism (a) = 13cm
height of prism (h) = 5 cm
diameter of circle(d) = 6 cm
To find:
Volume of prism =?
Solution:
Formula that would be used,
[tex] \sf volume \: of \: square \: prism = {a}^{2} h[/tex]
[tex] \sf volume \: of \: cylinder = \pi {r}^{2} h[/tex]
Let's calculate the overall volume of prism,
Volume of prism(including volume of hole) V = a²h
[tex] V = a²h \\ V = {13}^{2} \times 5 \\ V = 845 \: {cm}^{3} [/tex]
To find out the volume circular hole we need to find the radius of hole, since the diameter of hole is given we can calculate the radius by multiplying 1/2.
[tex]r= \frac{d}{2} \\ r = \frac{6}{2} \\ r = 3 \: cm[/tex]
now calculate the volume of circular hole inside the prism,
Volume of circular hole(cylindrical shape) v= πr²h
[tex]v = \pi {r}^{2} h \\ v = 3.14× {3}^{2} ×5 \\ v = 141.3 \: {cm}^{3}[/tex]
The volume of given diagram of prism (V') = Volume of overall prism(V) - volume of circular hole(v)
[tex]V' = V- v \\ V' = 845 - 141.3 \: \\ V' = 703.7 \: {cm}^{3}[/tex]
Answer - Volume of prism is 703.7 cm³
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Joshia starts with 100 In savings and saves 5 per week
Answer:
If you're asking for an equation to use for this problem you can use: 100+5x,
x is the number of weeks.
Step-by-step explanation:
You are starting with $100, and gain 5 dollars every week, so 100+5(#ofweeks)= total amount of money.
Teresa is maintaining a camp fire. She can
keep the fire burning for 4 hours with 6 logs.
She wants to know how many logs (y) she
needs to keep the fire burning for 18 hours.
She assumes all logs are the same.
How many logs does Teresa need to
maintain the fire for 18 hours?
Answer:
27
Step-by-step explanation:
she needs 24 logs to keep the fire for 16 hours(4×6). And for next 2 hours she's gonna need 3. altogether it's 27.
I really need help on this math problem, pls anyone that can help?!
Answer:
y = 3/2x + 6
Step-by-step explanation:
Equation of the given line
slope = rise/run = -2/3y-intercept = (0, -2)Equation is y = -2/3x - 2Perpendicular
Slope is the negative reciprocalm ⇒ -(1/[-2/3]) = 3/2Intersection point is (-2, 3)Using Point-slope equation
y - 3 = 3/2 (x + 2)y - 3 = 3/2x + 3y = 3/2x + 6Please solve (17 points)
Answer:
50.6
Step-by-step explanation:
Solve for x. Round to the nearest tenth.
Answer:
x= 11.87
Step-by-step explanation:
sec(32) = 14 /x
1.18=14/x
x1.18 =14
x= 11.87
If there are 12 people, and each person has 3 coins, there are ____ times as many coins as people
Answer:
Step-by-step explanation:
If x=−4 is a solution to the equation x2+11x+K=0 , then K= ?
Answer:
x^2 + 11x + k = 0
(-4) ^2 + 11 (-4) + k = 0
16 - 44 + k = 0
-28 + k = 0
K = 28
Hope Helpful ~
Figure ABCD is a parallelogram.What are the lengths of line segments AB and BC?
Answer:
I need an image
Step-by-step explanation:
Answer:CPCTC
Step-by-step explanation:
6. AB ≅ CD Corresponding Parts of Congruent triangles are Congruent(CPCTC)
Hope it helps:)
I need help on question b
Answer:
B=25
Step-by-step explanation:
Simply plug in 10 where x is
2(10)2(10-5)/10(10) = 25
What is the measure of n?
m
n
8
4
ከ =
4V[?]
Give your answer in simplest form.
Enter
The value of n is 32 if the total; base length is 12(8+4) and n is the length of the perpendicular.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We can use the altitude rule:
8/n = n/4
n² = 32
n = √32
Thus, the value of n is 32 if the total; base length is 12(8+4) and n is the length of the perpendicular.
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find the volume of this figure. round your answer to the nearest hundredth. if necessary
radius=8m
height=12m
#3
PLEASE HELP AREA QUESTION 40 POINTS
Answer:
14 meters
Step-by-step explanation:
